Here are the solutions for the worksheet, broken down by section.
Section A
*Work out the information indicated in the boxes.*
1. Data Set: 1, 2, 3, 6, 7, 8, 9
*
Median: The middle number is
6.
*
LQ (Lower Quartile): The median of the lower half (1, 2, 3) is
2.
*
UQ (Upper Quartile): The median of the upper half (7, 8, 9) is
8.
*
IQR (Interquartile Range): $8 - 2 =$
6.
2. Data Set: 5, 7, 5, 6, 4, 3, 9
*(First, sort the numbers: 3, 4, 5, 5, 6, 7, 9)*
*
Median: The middle number is
5.
*
LQ: The median of the lower half (3, 4, 5) is
4.
*
UQ: The median of the upper half (6, 7, 9) is
7.
*
IQR: $7 - 4 =$
3.
3. Data Set: 6, 9, 10, 10, 11, 15, 21, 26
*(Already sorted. There are 8 numbers, so we split them into two groups of 4)*
*
Median: Average of the two middle numbers (10 and 11). $(10+11)/2 =$
10.5.
*
LQ: Median of the first half (6, 9, 10, 10). Average of 9 and 10 is
9.5.
*
UQ: Median of the second half (11, 15, 21, 26). Average of 15 and 21 is
18.
*
IQR: $18 - 9.5 =$
8.5.
4. Data Set: 3, 9, 4, 3, 8, 9, 6, 3
*(First, sort the numbers: 3, 3, 3, 4, 6, 8, 9, 9)*
*
Median: Average of the two middle numbers (4 and 6). $(4+6)/2 =$
5.
*
IQR:
* LQ (median of 3, 3, 3, 4) = 3.
* UQ (median of 6, 8, 9, 9) = 8.5.
* IQR = $8.5 - 3 =$
5.5.
*
Range: Highest (9) - Lowest (3) =
6.
*
Mode: The most common number is
3.
5. Data Set: 14, 29, 24, 14, 13, 5, 21, 14, 13
*(First, sort the numbers: 5, 13, 13, 14, 14, 14, 21, 24, 29)*
*
Median: The middle number (5th one) is
14.
*
IQR:
* LQ (median of 5, 13, 13, 14) = 13.
* UQ (median of 14, 21, 24, 29) = 22.5.
* IQR = $22.5 - 13 =$
9.5.
*
Range: Highest (29) - Lowest (5) =
24.
*
Mode: The most common number is
14.
---
Section B
*Using the stem and leaf diagram complete the missing information.*
Diagram 1
*(Key: 4 | 2 represents 42)*
*Data list: 31, 46, 47, 50, 54, 55, 62, 67, 68, 72, 72, 73, 75, 76, 76, 76, 81, 82, 84, 85, 87, 93, 98*
*Total count ($n$): 23*
*
Highest value: 98
*
Lowest value: 31
*
Mode: The number appearing most often is
76.
*
Range: $98 - 31 =$
67
*
Median: The 12th number in the ordered list is
73.
*
IQR:
* LQ (6th number):
55
* UQ (18th number):
82
* IQR: $82 - 55 =$
27
Diagram 2
*(Key: 3 | 4 represents 3.4 kg)*
*Data list: 0.4, 1.2, 1.5, 1.8, 2.0, 2.2, 2.4, 2.6, 2.7, 2.8, 2.8, 3.1, 3.2, 3.3, 3.6, 3.8, 4.0, 4.2, 4.4, 5.5, 5.8*
*Total count ($n$): 21*
*
Highest value: 5.8
*
Lowest value: 0.4
*
Mode: The number appearing most often is
2.8.
*
Range: $5.8 - 0.4 =$
5.4
*
Median: The 11th number in the ordered list is
2.8.
*
IQR:
* LQ (5th number):
2.0
* UQ (16th number):
3.8
* IQR: $3.8 - 2.0 =$
1.8
──────────────────────────────────────
Final Answer:
Section A
1. Median:
6, LQ:
2, UQ:
8, IQR:
6
2. Median:
5, LQ:
4, UQ:
7, IQR:
3
3. Median:
10.5, LQ:
9.5, UQ:
18, IQR:
8.5
4. Median:
5, IQR:
5.5, Range:
6, Mode:
3
5. Median:
14, IQR:
9.5, Range:
24, Mode:
14
Section B
Top Diagram:
Highest:
98, Lowest:
31, Mode:
76, Range:
67, Median:
73, IQR:
27
Bottom Diagram:
Highest:
5.8, Lowest:
0.4, Mode:
2.8, Range:
5.4, Median:
2.8, IQR:
1.8
Parent Tip: Review the logic above to help your child master the concept of iqr worksheet.
