The table shows the heights of 40 students in a class. Height (h)
Frequency
in cm
120 <t< 124
7
124 <t< 128
8
128 <t< 132
13
132 <t< 136
9
136 <t< 140
3
a) Calculate an estimate for the mean height of the students.
b) Explain why your answer to part (a) is an estimate.

see below

Step-by-step explanation:

There are 7 students between 120 and 124 so take the median of 122

Multiply the number of students by the median

7 * 122 =854

There are 8 students between 124 and 128 so take the median of 126

Multiply the number of students by the median

8 * 126 =1008

There are 13 students between 128 and 132 so take the median of 130

Multiply the number of students by the median

13 * 130 =1690

There are 9 students between 132 and 136 so take the median of 134

Multiply the number of students by the median

9 * 134=1206

There are 3 students between 136 and 140 so take the median of 138

Multiply the number of students by the median

3 * 138 =414

To find the mean, take the total weight and divide by the number of students

(854+1008+1690+1206+414) = 5172 lbs

7+8+13+9+3 = 40 students

5172/40 =129.3 lbs for the average

This is an estimate because we do not know that the number of students in each category will weight the median on average.  We use the mean as an estimate of their weight.  The median is the middle number of the category.