Basil asks each of 40 students how many books they bought last year. The chart shows information about the number of books they each bought.

144

a) What is the percentage

12

of these students who

bought 20 or more books? (2)

10-

15%

Number

of

b) Work out an estimate for the

students

mean number of books bought.

8

6

4

2

0

0 to 4

5 to 9 10 to 14 15 to 19 20 to 24

Number of books

(4)

Total marks: 6

Answer/Step-by-step Explanation:

We are given the chart attached below showing no. of books bought by each of the 40 students.

=>Required:

a. % of students who bought 20 or more books (20-24 books)

b. Show that the estimated mean no. of books = 9.5 (i.e. we are to show/calculate the estimated mean for the data given which should be 9.5)

==>SOLUTION:

a. % of students who bought 20 - 24 books = no of students who bought 20-24 books ÷ total number of students multiplied by 100

From the chart, checking the column that represents 20-24, we have 2 students who bought 20 or more books.

Therefore, % of students who bought 20 or more books =

=

= 5%

b. To calculate the estimated mean no. of books bought, which should give us 9.5, we would use the formula μ = (∑mf)/N

Where μ = estimated mean

∑ = summation

m = class midpoint

f = frequency

N = population

Estimated mean can be calculated in 3 simple steps as follows:

=>STEP 1: Find mid-point of each class (i.e. m). Thus,

Class 0 - 4 = 2

Class 5 - 9 = 7

Class 10 - 14 = 12

Class 15 - 19 = 17

Class 20 - 24 = 22

STEP 2: Multiply each mid-point by its corresponding class frequency (i.e. mf). Thus,

For Class 0 - 4, we have (2)(11) = 22

For Class 5 - 9, we have (7)(8) = 56

For Class 10 - 14, we have (12)(13) = 156

For Class 15 - 19, we have (17)(6) = 102

For, Cass 20 - 24, we have (22)(2) = 44

STEP 3: Add each value we got from Step 2 and divide by 40 i.e.

Thus,

=

= 9.5

Estimated mean (μ) = 9.5

goog may have it for you