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 = [tex]\frac{2}{40}*100[/tex]
= [tex]\frac{200}{40}[/tex]
= 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. [tex]\frac{∑mf}{N}[/tex]
Thus,
[tex]\frac{22 + 56 + 156 + 102 + 44}{40}[/tex]
= [tex]\frac{380}{40}[/tex]
= 9.5
Estimated mean (μ) = 9.5
