Question

The histogram represents ages of 40 people at a store that sells children's clothes. Which interval contains the median? Histogram from 0 to 35 by 5’s. age (years). Beginning at 0 up to but not including 5, height of bar at each interval is 10, 8, 6, 3, 5, 3, 4. A: The interval from 0 to 5 years. B: The interval from 5 to 10 years. C: The interval from 10 to 15 years. D: The interval from 15 to 20 years.​

Answer 1

Answer:

Option C.

Step-by-step explanation:

It is given that a histogram from 0 to 35 by 5’s. age (years). Beginning at 0 up to but not including 5, height of bar at each interval is 10, 8, 6, 3, 5, 3, 4.

The frequency table is:

Class interval     frequency table       Cumulative frequency

        0-5                  10                                    10

        5-10                  8                                    18

       10-15                  6                                    24        Median class

      15-20                  3                                    27

      20-25                  5                                   32

      25-30                  3                                   35

      30-35                  4                                   39

Sum of frequencies is 39, which is an odd number.

$Median=\dfrac{n+1}{2}\text{th term}$

$Median=\dfrac{39+1}{2}\text{th term}$

$Median=\dfrac{40}{2}\text{th term}$

$Median=20\text{th term}$

Now, we need a class whose cumulative frequency is more than 20 but its previous cumulative frequency is less than 20.

Median class is 10-15 because cumulative frequency of class 10-15 is 24. So 20th term is in the class 10-15.

Therefore, the correct option is C.