Statistical analysis of housing data in Excel, including house age, distance to station, and price per square foot.

Let’s solve this step by step.

We are given a column of “Price per Square Foot” values (Column C, rows 2 to 15). We need to calculate:

- Median
- Mode
- Standard Deviation
- Variance

First, let’s list all the Price per Square Foot values from Column C (rows 2 to 15):

75.8
84.4
94.6
109.6
86.2
64.2
80.6
93.4
37.6
44.2
82.8
116.2
78.6
47.6

That’s 14 numbers total.

---

Step 1: Find the Median

Median is the middle value when numbers are sorted in order.

Sort the list:

37.6, 44.2, 47.6, 64.2, 75.8, 78.6, 80.6, 82.8, 84.4, 86.2, 93.4, 94.6, 109.6, 116.2

There are 14 numbers → even count → median = average of 7th and 8th values.

7th value = 80.6
8th value = 82.8
Median = (80.6 + 82.8) / 2 = 163.4 / 2 = 81.7

✔ Median = 81.7

---

Step 2: Find the Mode

Mode is the number that appears most often.

Look at the original list:

75.8, 84.4, 94.6, 109.6, 86.2, 64.2, 80.6, 93.4, 37.6, 44.2, 82.8, 116.2, 78.6, 47.6

All values appear only once → no repeats → no mode

In Excel or statistics, if there’s no repeating value, we say “No Mode” or leave blank. But sometimes systems expect you to write “N/A” or just leave empty. Since the table has an empty cell for Mode, and no value repeats, we’ll put:

✔ Mode = No Mode (or leave blank — but since it’s a homework problem, likely they want “No Mode” or perhaps check if any repeat? Let’s double-check.)

Wait — look again:

Original data:

Row 2: 75.8
Row 3: 84.4
Row 4: 94.6
Row 5: 109.6
Row 6: 86.2
Row 7: 64.2
Row 8: 80.6
Row 9: 93.4
Row 10: 37.6
Row 11: 44.2
Row 12: 82.8
Row 13: 116.2
Row 14: 78.6
Row 15: 47.6

No duplicates → so no mode

But wait — maybe I miscounted? Let me sort them again and check for duplicates:

Sorted:
37.6, 44.2, 47.6, 64.2, 75.8, 78.6, 80.6, 82.8, 84.4, 86.2, 93.4, 94.6, 109.6, 116.2

Still all unique → ✔ Mode = No Mode

However, in some contexts, especially Excel, if no mode exists, MODE function returns #N/A. But since this is a worksheet with manual entry, and the student is expected to fill it, probably they should write “No Mode” or leave blank. But looking at the Sum and Mean already filled, and others blank — likely they expect numerical answers where possible.

Wait — actually, let me check if any value repeats… NO. So Mode does not exist.

But perhaps the problem expects us to use Excel functions? The screenshot shows Excel interface. In Excel, =MODE(C2:C15) would return #N/A because no duplicate.

But since this is a homework problem, and the other stats are being calculated manually or via formula, perhaps we should note “No Mode”.

Alternatively — did I miss something?

Wait — Row 4 and Row 5 both have House Age 13.3 — but that’s Column A, not Price. We’re only looking at Column C for Price per Square Foot.

So yes — no repeated price → no mode.

✔ Final decision: Mode = No Mode (but since the box is empty and others are numbers, maybe leave blank? Or write “None”? For accuracy, we’ll state “No Mode”)

But let’s see what the problem expects — since Sum and Mean are given as numbers, and others are blank, likely they want numbers where possible. Since no mode, we can write “N/A” or leave blank. But to be precise, I’ll write “No Mode” in reasoning, but for final answer box, perhaps leave as blank? Wait — the instruction says “solve the problem accurately”, so we must report correctly.

Actually, in many school settings, if no mode, they accept “no mode” or “none”. I’ll go with “No Mode”.

But let’s hold on — maybe I made a mistake? Let me count frequency:

List again:

75.8 — 1
84.4 — 1
94.6 — 1
109.6 — 1
86.2 — 1
64.2 — 1
80.6 — 1
93.4 — 1
37.6 — 1
44.2 — 1
82.8 — 1
116.2 — 1
78.6 — 1
47.6 — 1

Yes, all once → no mode.

✔ Mode = No Mode

---

Step 3: Find Standard Deviation

Standard deviation measures how spread out the numbers are.

Formula for sample standard deviation (since this is a sample of houses, not entire population):

s = √[ Σ(xi - x̄)² / (n - 1) ]

We already know the mean (x̄) = 76.94 (given in E4)

n = 14

So we need to:

1. Subtract mean from each value → get deviations
2. Square each deviation
3. Sum those squared deviations
4. Divide by (n - 1) = 13 → that’s variance
5. Take square root → standard deviation

Let’s compute step by step.

First, list all values and subtract mean (76.94), then square.

I’ll make a table:

Value | Deviation (x - mean) | Squared Deviation
------|----------------------|------------------
75.8 | 75.8 - 76.94 = -1.14 | (-1.14)^2 = 1.2996
84.4 | 84.4 - 76.94 = 7.46 | 55.6516
94.6 | 94.6 - 76.94 = 17.66 | 311.8756
109.6 | 109.6 - 76.94 = 32.66| 1066.6756
86.2 | 86.2 - 76.94 = 9.26 | 85.7476
64.2 | 64.2 - 76.94 = -12.74| 162.3076
80.6 | 80.6 - 76.94 = 3.66 | 13.3956
93.4 | 93.4 - 76.94 = 16.46 | 270.9316
37.6 | 37.6 - 76.94 = -39.34| 1547.6356
44.2 | 44.2 - 76.94 = -32.74| 1071.9076
82.8 | 82.8 - 76.94 = 5.86 | 34.3396
116.2 | 116.2 - 76.94 = 39.26| 1541.3476
78.6 | 78.6 - 76.94 = 1.66 | 2.7556
47.6 | 47.6 - 76.94 = -29.34| 860.8356

Now sum all squared deviations:

Let’s add them step by step:

Start with 0.

+1.2996 = 1.2996
+55.6516 = 56.9512
+311.8756 = 368.8268
+1066.6756 = 1435.5024
+85.7476 = 1521.25
+162.3076 = 1683.5576
+13.3956 = 1696.9532
+270.9316 = 1967.8848
+1547.6356 = 3515.5204
+1071.9076 = 4587.428
+34.3396 = 4621.7676
+1541.3476 = 6163.1152
+2.7556 = 6165.8708
+860.8356 = 7026.7064

So sum of squared deviations = 7026.7064

Now, divide by (n - 1) = 13 → this is the sample variance.

Variance = 7026.7064 / 13 ≈ ?

Calculate: 7026.7064 ÷ 13

13 * 540 = 7020 → remainder 6.7064

6.7064 / 13 ≈ 0.5158769

So variance ≈ 540 + 0.5158769 ≈ 540.5158769

More precisely:

7026.7064 ÷ 13 = let's do exact division:

13 * 540.515876923...

Actually, better to compute:

7026.7064 / 13 = 540.515876923...

So variance ≈ 540.5159 (rounded to 4 decimals)

But let’s keep more precision for now.

Actually, let me verify the sum of squared deviations because it’s critical.

I could use another way: use the fact that sum of squares can also be computed as:

Σ(x_i²) - n*(mean)²

But we don’t have sum of squares directly. Alternatively, trust our calculation.

But let me cross-check one or two:

For example, 37.6: (37.6 - 76.94)^2 = (-39.34)^2 = 1547.6356 — correct.

116.2: (116.2 - 76.94)=39.26^2=1541.3476 — correct.

Sum seems right.

So variance = 7026.7064 / 13 = 540.515876923...

≈ 540.5159

Now standard deviation = sqrt(variance) = sqrt(540.515876923)

Compute square root:

What’s sqrt(540.5159)?

Well, 23^2 = 529
24^2 = 576
So between 23 and 24.

23.2^2 = 538.24
23.3^2 = 542.89
Too big.

23.25^2 = (23 + 0.25)^2 = 23^2 + 2*23*0.25 + 0.25^2 = 529 + 11.5 + 0.0625 = 540.5625

Our variance is 540.5159, which is slightly less than 540.5625.

So sqrt(540.5159) ≈ 23.248 or so.

Compute difference: 540.5625 - 540.5159 = 0.0466

Derivative: d(sqrt)/dx = 1/(2*sqrt(x)) ≈ 1/(2*23.25) ≈ 1/46.5 ≈ 0.0215

So adjustment: -0.0466 * 0.0215 ≈ -0.001

So approx 23.25 - 0.001 = 23.249

Better to use calculator, but since this is text, let’s compute:

23.24^2 = (23 + 0.24)^2 = 529 + 2*23*0.24 + 0.24^2 = 529 + 11.04 + 0.0576 = 540.0976

Too low.

23.25^2 = 540.5625 as above.

Target: 540.5159

Difference from 23.24^2: 540.5159 - 540.0976 = 0.4183

Increment from 23.24 to 23.25 is 0.01, and square increases by 540.5625 - 540.0976 = 0.4649

So fraction: 0.4183 / 0.4649 ≈ 0.8997

So add 0.8997 * 0.01 ≈ 0.008997 to 23.24 → 23.248997

So approximately 23.249

Thus, standard deviation ≈ 23.249

But let’s use more precise calculation.

Actually, in Excel, if you input these numbers, STDEV.S would give the sample standard deviation.

Since we have the sum of squared deviations = 7026.7064, n=14, so variance = 7026.7064 / 13 = 540.5158769230769

Then std dev = sqrt(540.5158769230769) = ?

Compute: 23.248999... let’s say 23.249

But to be accurate, let’s calculate:

23.249^2 = 23.249 * 23.249

23^2=529
0.249*23*2 = 0.249*46 = let's compute: 0.25*46=11.5, minus 0.001*46=0.046, so 11.5 - 0.046=11.454? No:

(a+b)^2 = a^2 + 2ab + b^2, a=23, b=0.249

a^2=529
2ab=2*23*0.249=46*0.249

46*0.25=11.5, 46*0.001=0.046, so 46*0.249=46*(0.25-0.001)=11.5 - 0.046=11.454

b^2=0.249^2=0.062001

Total: 529 + 11.454 + 0.062001 = 540.516001

Which is very close to 540.5158769 — difference is about 0.000124, negligible.

So std dev ≈ 23.249

We can round to two decimals as per the given mean (76.94 has two decimals).

Given mean is 76.94, sum is 3847.20 — both to two decimals.

So probably report std dev and variance to two decimals.

Variance = 540.5159 ≈ 540.52

Std dev = 23.249 ≈ 23.25

Check: 23.25^2 = 540.5625, which is higher than 540.5159, so 23.25 is a bit high.

23.24^2 = as before, 540.0976

Interpolate:

Target variance: 540.5159

At 23.24: 540.0976
At 23.25: 540.5625
Difference: 0.4649 for 0.01 increase

Need to go up by 540.5159 - 540.0976 = 0.4183

Fraction: 0.4183 / 0.4649 ≈ 0.8997

So std dev = 23.24 + 0.008997 ≈ 23.249

So to two decimals, it’s 23.25? But 23.25^2=540.5625 > 540.5159, so perhaps 23.25 is acceptable rounding, or 23.24?

23.249 rounded to two decimals is 23.25.

Similarly, variance 540.5159 to two decimals is 540.52.

But let’s confirm with actual Excel calculation mentally.

I recall that in such problems, sometimes they expect population standard deviation, but the context is sample of houses, so sample std dev is appropriate.

The given mean is 76.94, which matches: sum is 3847.20, divided by 14 = 3847.20 / 14 = ?

14 * 274 = 3836, remainder 11.20, 11.20/14=0.8, so 274.8? No:

3847.20 ÷ 14

14 * 274 = 3836
3847.20 - 3836 = 11.20
11.20 / 14 = 0.8
So 274 + 0.8 = 274.8? That can’t be right because prices are around 70-100.

Mistake!

Sum is 3847.20 for 14 values? But earlier I listed the values, let me sum them to verify.

List of prices:

75.8
84.4
94.6
109.6
86.2
64.2
80.6
93.4
37.6
44.2
82.8
116.2
78.6
47.6

Add them:

Group:

75.8 + 84.4 = 160.2
+94.6 = 254.8
+109.6 = 364.4
+86.2 = 450.6
+64.2 = 514.8
+80.6 = 595.4
+93.4 = 688.8
+37.6 = 726.4
+44.2 = 770.6
+82.8 = 853.4
+116.2 = 969.6
+78.6 = 1048.2
+47.6 = 1095.8

That’s only 1095.8? But the sum given is 3847.20 — that doesn't match.

I think I made a huge mistake.

Look back at the image description.

The user said: "uploaded an image", and in the image, Column C is "Price per Square Foot", and rows 2 to 15 have values, but in my initial list, I took only 14 values, but let's count the rows.

Rows 2 to 15 inclusive is 14 rows, but the sum given is 3847.20, and mean 76.94, so 3847.20 / 14 = 274.8, which is not matching my sum of 1095.8.

This means I must have misread the values.

Let me look back at the user's message.

In the text, it says:

C2: 75.8
C3: 84.4
C4: 94.6
C5: 109.6
C6: 86.2
C7: 64.2
C8: 80.6
C9: 93.4
C10: 37.6
C11: 44.2
C12: 82.8
C13: 116.2
C14: 78.6
C15: 47.6

Sum of these: let's calculate again carefully.

75.8 + 84.4 = 160.2
160.2 + 94.6 = 254.8
254.8 + 109.6 = 364.4
364.4 + 86.2 = 450.6
450.6 + 64.2 = 514.8
514.8 + 80.6 = 595.4
595.4 + 93.4 = 688.8
688.8 + 37.6 = 726.4
726.4 + 44.2 = 770.6
770.6 + 82.8 = 853.4
853.4 + 116.2 = 969.6
969.6 + 78.6 = 1048.2
1048.2 + 47.6 = 1095.8

But the sum in E2 is 3847.20, which is much larger.

Perhaps I missed some rows? Rows 2 to 15 is 14 rows, but maybe there are more? No, the table shows up to row 15.

Unless the "Price per Square Foot" includes more values, but in the text, only those are listed.

Perhaps the sum 3847.20 is for a different column? No, E2 is labeled "Sum", and F2 has 3847.20, and E4 has "Mean" with 76.94, and 3847.20 / 14 = 274.8, not 76.94.

76.94 * 14 = ? 70*14=980, 6.94*14=97.16, total 1077.16, close to my 1095.8? Not really.

76.94 * 14 = let's calculate: 77*14 = 1078, but 76.94*14 = 76.94*10=769.4, 76.94*4=307.76, total 769.4+307.76=1077.16

But my sum is 1095.8, which is different.

This suggests that either the values are wrong, or I have a mistake in reading the image.

Perhaps the "Price per Square Foot" values are not what I think.

Let me read the user's input again.

In the text, it says:

" C ' " and then values, but perhaps the values are for different columns.

Another possibility: the sum 3847.20 is for the "Distance to Station" or "House Age", but no, E2 is next to "Sum", and F2 has 3847.20, and E4 has "Mean" with 76.94, which matches the price per square foot mean if sum is around 1077, but 3847.20 is given.

Unless the number of data points is not 14.

Let's count the rows with data in Column C.

From the text:

Row 2: 75.8
Row 3: 84.4
Row 4: 94.6
Row 5: 109.6
Row 6: 86.2
Row 7: 64.2
Row 8: 80.6
Row 9: 93.4
Row 10: 37.6
Row 11: 44.2
Row 12: 82.8
Row 13: 116.2
Row 14: 78.6
Row 15: 47.6

That's 14 values.

But 14 * 76.94 = 1077.16, but given sum is 3847.20, which is roughly 3.5 times larger.

Perhaps the values are in different units, or I misread the numbers.

Another idea: perhaps the "Price per Square Foot" values are larger, but in the text, it's written as 75.8 etc, but maybe it's 758 or something, but that doesn't make sense.

Let's look at the distance to station: B2: 84.87882, B3: 306.5947, etc, sum of those might be large.

Sum of distance to station: let's estimate.

B2: 84.88
B3: 306.59
B4: 561.98
B5: 561.98
B6: 390.57
B7: 2175.03
B8: 623.47
B9: 287.60
B10: 5512.04
B11: 1783.18
B12: 405.21
B13: 90.46
B14: 492.23
B15: 2469.65

This will be large. Let's approximate:

84 + 306 = 390
+562 = 952
+562 = 1514
+391 = 1905
+2175 = 4080
+623 = 4703
+288 = 4991
+5512 = 10503
+1783 = 12286
+405 = 12691
+90 = 12781
+492 = 13273
+2470 = 15743

So around 15743, not 3847.

House age: A2: 32, A3: 19.5, A4: 13.3, A5: 13.3, A6: 5, A7: 7.1, A8: 34.5, A9: 20.3, A10: 31.7, A11: 17.9, A12: 34.8, A13: 6.3, A14: 13, A15: 20.4

Sum: 32+19.5=51.5; +13.3=64.8; +13.3=78.1; +5=83.1; +7.1=90.2; +34.5=124.7; +20.3=145; +31.7=176.7; +17.9=194.6; +34.8=229.4; +6.3=235.7; +13=248.7; +20.4=269.1

Not 3847.

So what is 3847.20? Perhaps it's the sum of price per square foot, but my calculation gives 1095.8, while 3847.20 / 14 = 274.8, which is not matching.

Unless there are more rows. The table shows up to row 15, but perhaps there are hidden rows or something.

Another possibility: the "Price per Square Foot" values are for more than 14 rows, but in the text, only 14 are listed.

Perhaps I need to use the given sum and mean to find the number of data points.

Given sum = 3847.20, mean = 76.94, so number of data points n = sum / mean = 3847.20 / 76.94

Calculate that: 3847.20 ÷ 76.94

First, 76.94 * 50 = 3847, exactly? 76.94 * 50 = 3847.00, and 3847.20 - 3847.00 = 0.20, so 50 + 0.20/76.94 ≈ 50 + 0.0026 = 50.0026, so approximately 50.

76.94 * 50 = 3847.00, and sum is 3847.20, so n = 50.0026, not integer.

76.94 * 50 = 3847.00, but sum is 3847.20, so perhaps n=50, and mean is approximate.

3847.20 / 50 = 76.944, which rounds to 76.94, so likely n=50.

But in the table, only 14 rows are shown with data in Column C. This suggests that there are more rows below row 15 that are not visible in the image, or perhaps the data continues.

In the user's text, it says "rows 2 to 15", but perhaps in the actual image, there are more rows.

Looking back at the user's message: "C2: 75.8" to "C15: 47.6", but maybe there are C16 to C51 or something.

Perhaps the "Price per Square Foot" has 50 values, but only first 14 are listed in the text description.

This is a problem.

Perhaps the sum 3847.20 is for the entire column, and we have to assume that the mean is given, and we need to calculate median, mode, etc for the full dataset, but we only have partial data.

That doesn't make sense for a homework problem.

Another idea: perhaps the values in Column C are not the only ones; maybe the table has more rows, but in the text, only up to 15 are provided, but for the sake of the problem, we should use the given sum and mean, and perhaps the median, mode, etc can be calculated from the given 14 values, but then the sum wouldn't match.

Perhaps the 3847.20 is a typo, and it should be 1077.16 or something.

Let's calculate the sum of the 14 values I have: 1095.8, and 1095.8 / 14 = 78.2714, but given mean is 76.94, close but not exact.

76.94 * 14 = 1077.16, as before.

My sum is 1095.8, which is higher.

Let me double-check the addition of the 14 values.

List again:

1. 75.8
2. 84.4 -> 75.8+84.4=160.2
3. 94.6 -> 160.2+94.6=254.8
4. 109.6 -> 254.8+109.6=364.4
5. 86.2 -> 364.4+86.2=450.6
6. 64.2 -> 450.6+64.2=514.8
7. 80.6 -> 514.8+80.6=595.4
8. 93.4 -> 595.4+93.4=688.8
9. 37.6 -> 688.8+37.6=726.4
10. 44.2 -> 726.4+44.2=770.6
11. 82.8 -> 770.6+82.8=853.4
12. 116.2 -> 853.4+116.2=969.6
13. 78.6 -> 969.6+78.6=1048.2
14. 47.6 -> 1048.2+47.6=1095.8

Yes.

But 1095.8 vs expected 1077.16 for mean 76.94.

Difference of 18.64, which is significant.

Perhaps one of the values is misread.

For example, if C5 is 109.6, but maybe it's 90.6 or something.

Or C13 is 116.2, maybe 96.2.

But without the actual image, it's hard.

Perhaps the "Price per Square Foot" includes values from other rows, but in the text, only these are given.

Another thought: in the image, there might be more rows, but the user only described up to row 15.

Perhaps for the purpose of this problem, we should use the given sum and mean, and assume that the data is as given, but then the sum doesn't match.

Let's look at the given mean: 76.94, and sum 3847.20, so n = 3847.20 / 76.94 = let's calculate accurately.

3847.20 ÷ 76.94

First, 76.94 * 50 = 3847.00, as 70*50=3500, 6.94*50=347, total 3847.00

3847.20 - 3847.00 = 0.20, so n = 50 + 0.20/76.94 ≈ 50 + 0.0026 = 50.0026, not integer.

76.94 * 50 = 3847.00, but sum is 3847.20, so perhaps the mean is rounded, and actual mean is 3847.20 / 50 = 76.944, which rounds to 76.94.

So likely, there are 50 data points, and the mean is 76.944, reported as 76.94.

But in the table, only 14 values are shown, so for median, mode, etc, we need all 50 values, which we don't have.

This is a dilemma.

Perhaps the 3847.20 is for a different column, but the label "Sum" is in E2, and F2 has 3847.20, and E4 has "Mean" with 76.94, and since 3847.20 / 50 = 76.944 ≈ 76.94, and 50 is a nice number, likely n=50.

But then how to find median, mode, etc with only 14 values? We can't.

Unless the problem is to use the given 14 values for calculation, and ignore the sum and mean given, but that doesn't make sense because the sum and mean are provided for verification.

Perhaps the sum 3847.20 is for the "Distance to Station" or "House Age", but as calculated, house age sum is around 269, distance is around 15743, not 3847.

Another idea: perhaps "Price per Square Foot" is in dollars, and the values are correct, but the sum is for a different thing.

Let's calculate the sum of the 14 values: 1095.8, and if we take that as sum, mean = 1095.8 / 14 = 78.2714, but given mean is 76.94, so not match.

Perhaps there is a mistake in the problem, or in my reading.

Let's try to see if the given mean 76.94 matches if we use the values.

Perhaps the values are for C2 to C51, but only C2 to C15 are listed.

For the sake of progressing, perhaps in this context, we should use the 14 values given, and calculate based on that, and assume that the sum and mean given are for those 14, but they don't match, so maybe the sum 3847.20 is a typo, and it should be 1077.16 or 1095.8.

Notice that 76.94 * 14 = 1077.16, and my sum is 1095.8, difference of 18.64.

If I adjust one value, e.g., if C5 is 90.6 instead of 109.6, then sum would be 1095.8 - 19 = 1076.8, close to 1077.16.

109.6 - 90.6 = 19, so if C5 is 90.6, sum = 1095.8 - 19 = 1076.8, and 1076.8 / 14 = 76.914, close to 76.94.

Or if C13 is 96.2 instead of 116.2, difference 20, sum 1075.8, mean 76.842, not as good.

Perhaps C4 is 74.6 instead of 94.6, difference 20, sum 1075.8, same.

But without knowing, it's guesswork.

Perhaps the "109.6" is "90.6", but in the text, it's written as 109.6.

Another possibility: the sum 3847.20 is for the product or something, but unlikely.

Let's look at the variance and std dev given in the table; they are blank, so we need to calculate.

Perhaps for this problem, we are to use the 14 values as given, and calculate median, mode, std dev, variance for those 14, and ignore the sum and mean given, or use them as is.

But the mean is given as 76.94, which doesn't match our calculation.

Perhaps the mean 76.94 is for the 14 values, so sum should be 76.94 * 14 = 1077.16, so perhaps there is a typo in the values.

Let's assume that the sum is 1077.16 for 14 values, mean 76.94, and proceed with the values as given, but then when calculating std dev, use the given mean.

In statistics, when calculating variance, we can use the given mean if it's provided, even if it's rounded.

So perhaps for consistency, we should use the given mean 76.94 for calculations, even though the actual sum of the 14 values is 1095.8, but that would be inconsistent.

Perhaps the 14 values are correct, and the sum 3847.20 is for a different column, but the label "Sum" is in E2, and it's likely for Column C, as it's common to have summary statistics for the main variable.

Another idea: perhaps "Price per Square Foot" is in cents or something, but 75.8 cents doesn't make sense.

Let's calculate the sum of the 14 values again, but perhaps I missed that there are more values.

In the user's text, it says "C2: 75.8" to "C15: 47.6", but perhaps C1 to C1 or something, but C1 is header.

Perhaps row 1 is included, but C1 is "Price per Square Foot", not a number.

I think there's a mistake in the problem or in my understanding.

Perhaps the sum 3847.20 is the sum of all three columns or something, but that doesn't make sense.

Let's try to see the context. The user said "solve the problem accurately", and in the image, there are cells for Median, Mode, St. Deviation, Variance in E5 to E8, with F5 to F8 blank, so we need to fill those.

Given that, and since the sum and mean are given for Column C, likely for the full dataset, but we only have partial data.

Perhaps for this exercise, we are to use the 14 values provided, and calculate based on that, and the sum and mean given are for those 14, so perhaps the sum 3847.20 is a typo, and it should be 1077.16 or 1095.8.

Notice that 76.94 * 14 = 1077.16, and if we take that as sum, then for std dev, we can use that.

But our calculated sum is 1095.8, so perhaps in the actual image, the values are different.

Perhaps "109.6" is "90.6", as I thought earlier.

Let me assume that C5 is 90.6 instead of 109.6, then sum = 1095.8 - 19 = 1076.8, close to 1077.16.

1076.8 / 14 = 76.914, and given mean is 76.94, close enough for rounding.

Or if C5 is 90.6, and C13 is 116.2, etc.

To match exactly, 76.94 * 14 = 1077.16, so sum should be 1077.16.

Our sum is 1095.8, difference 18.64.

If we reduce C5 from 109.6 to 90.96, then difference 18.64, sum 1077.16.

But 90.96 is not nice.

Perhaps there is a value missing or extra.

Another possibility: perhaps there are 50 values, but only 14 are shown, and for the sake of the problem, we are to use the given mean and sum, but for median, we need the data.

This is not working.

Let's look online or think differently.

Perhaps the "3847.20" is the sum of the "Distance to Station" for the first few, but earlier calculation showed it's larger.

Let's calculate the sum of the distance to station for the 14 values:

B2: 84.87882
B3: 306.5947
B4: 561.9845
B5: 561.9845
B6: 390.5684
B7: 2175.03
B8: 623.4731
B9: 287.6025
B10: 5512.038
B11: 1783.18
B12: 405.2134
B13: 90.45606
B14: 492.2313
B15: 2469.645

Add them:

Start with 84.87882 + 306.5947 = 391.47352
+561.9845 = 953.45802
+561.9845 = 1515.44252
+390.5684 = 1906.01092
+2175.03 = 4081.04092
+623.4731 = 4704.51402
+287.6025 = 4992.11652
+5512.038 = 10504.15452
+1783.18 = 12287.33452
+405.2134 = 12692.54792
+90.45606 = 12783.00398
+492.2313 = 13275.23528
+2469.645 = 15744.88028

So approximately 15744.88, not 3847.20.

House age sum was 269.1, not 3847.

So only possibility is that "Price per Square Foot" has 50 values, sum 3847.20, mean 76.94, and the 14 values are a subset, but for median, we need all 50.

Since this is a homework problem, and likely the 14 values are intended, perhaps the sum 3847.20 is a mistake, and it should be 1077.16 or 1095.8.

Perhaps "3847.20" is for the variance or something, but it's in F2 under "Sum".

Another idea: perhaps the "Sum" is for the squared values or something, but unlikely.

Let's calculate the sum of squares of the 14 values.

From earlier, when I calculated for std dev, I had sum of squared deviations, but not sum of squares.

Sum of x_i^2 for the 14 values.

From the list:

75.8^2 = 5745.64
84.4^2 = 7123.36
94.6^2 = 8949.16
109.6^2 = 12012.16
86.2^2 = 7430.44
64.2^2 = 4121.64
80.6^2 = 6496.36
93.4^2 = 8723.56
37.6^2 = 1413.76
44.2^2 = 1953.64
82.8^2 = 6855.84
116.2^2 = 13502.44
78.6^2 = 6177.96
47.6^2 = 2265.76

Now sum these:

Let's add:

5745.64 + 7123.36 = 12869
+8949.16 = 21818.16
+12012.16 = 33830.32
+7430.44 = 41260.76
+4121.64 = 45382.4
+6496.36 = 51878.76
+8723.56 = 60602.32
+1413.76 = 62016.08
+1953.64 = 63969.72
+6855.84 = 70825.56
+13502.44 = 84328
+6177.96 = 90505.96
+2265.76 = 92771.72

So sum of squares = 92771.72

Then if mean is 76.94, sum of x_i = 76.94 * 14 = 1077.16

Then sum of (x_i - mean)^2 = sum x_i^2 - n*mean^2 = 92771.72 - 14*(76.94)^2

76.94^2 = 5919.7636

14*5919.7636 = 82876.6904

Then sum of squared deviations = 92771.72 - 82876.6904 = 9895.0296

Then variance = 9895.0296 / 13 = 761.1561230769

Std dev = sqrt(761.1561230769) = 27.5883, approximately 27.59

But this is using the given mean, not the actual mean of the data.

And the actual sum of the data is 1095.8, not 1077.16, so it's inconsistent.

Perhaps for the problem, we should use the actual data as given, and calculate everything from scratch, ignoring the given sum and mean, or using them as is.

But the given mean is 76.94, which is close to 78.27, so perhaps it's rounded.

Let's calculate the actual mean of the 14 values: 1095.8 / 14 = 78.27142857

Then for std dev, use this mean.

So mean = 78.271