Mean from a Frequency Table Textbook Exercise - Corbettmaths - Free Printable

To find the mean from a frequency table, we follow these steps:
1. Multiply each value by its frequency to get the total for that row.
2. Add up all those totals to get the Sum of Values.
3. Add up all the frequencies to get the Total Frequency (total number of items).
4. Divide the Sum of Values by the Total Frequency.

Here are the step-by-step solutions for each part:

(a) Age
* $5 \times 2 = 10$
* $6 \times 2 = 12$
* $7 \times 5 = 35$
* $8 \times 1 = 8$
* Sum: $10 + 12 + 35 + 8 = 65$
* Total Frequency: $2 + 2 + 5 + 1 = 10$
* Mean: $65 \div 10 = 6.5$

(b) Number of phones
* $0 \times 1 = 0$
* $1 \times 3 = 3$
* $2 \times 2 = 4$
* $3 \times 0 = 0$
* $4 \times 4 = 16$
* $5 \times 0 = 0$
* Sum: $0 + 3 + 4 + 0 + 16 + 0 = 23$
* Total Frequency: $1 + 3 + 2 + 0 + 4 + 0 = 10$
* Mean: $23 \div 10 = 2.3$

(c) Number of pets
* $0 \times 13 = 0$
* $1 \times 28 = 28$
* $2 \times 50 = 100$
* $3 \times 9 = 27$
* Sum: $0 + 28 + 100 + 27 = 155$
* Total Frequency: $13 + 28 + 50 + 9 = 100$
* Mean: $155 \div 100 = 1.55$

(d) Money Withdrawn
* $10 \times 16 = 160$
* $20 \times 19 = 380$
* $30 \times 4 = 120$
* $40 \times 3 = 120$
* $50 \times 6 = 300$
* $60 \times 2 = 120$
* Sum: $160 + 380 + 120 + 120 + 300 + 120 = 1200$
* Total Frequency: $16 + 19 + 4 + 3 + 6 + 2 = 50$
* Mean: $1200 \div 50 = 24$

(e) Number of bedrooms
* $1 \times 34 = 34$
* $2 \times 275 = 550$
* $3 \times 512 = 1536$
* $4 \times 179 = 716$
* Sum: $34 + 550 + 1536 + 716 = 2836$
* Total Frequency: $34 + 275 + 512 + 179 = 1000$
* Mean: $2836 \div 1000 = 2.836$

(f) Level
* $3 \times 1 = 3$
* $4 \times 9 = 36$
* $5 \times 7 = 35$
* $6 \times 2 = 12$
* $7 \times 1 = 7$
* Sum: $3 + 36 + 35 + 12 + 7 = 93$
* Total Frequency: $1 + 9 + 7 + 2 + 1 = 20$
* Mean: $93 \div 20 = 4.65$

Final Answer:
(a) 6.5
(b) 2.3
(c) 1.55
(d) £24
(e) 2.836
(f) 4.65