Question

Please help asap. find the mean median and mode ss below

Answer 1

The Mean is approximately 15.92. The Median is approximately 17.29 and the mode is 17.

Mean:

`\[ \text{Mean} = ((14 * 4) + (15 * 9) + (16 * 10) + (17 * 12) + (18 * 9) + (19 * 5) + (20 * 2))/(4 + 9 + 10 + 12 + 9 + 5 + 2) \]`

`\[ \text{Mean} = (56 + 135 + 160 + 204 + 162 + 95 + 40)/(51) \]`

`\[ \text{Mean} = (812)/(51) \]`

`\[ \text{Mean} \approx 15.92 \]`

Median:

To find the median, first, we need to identify the median class. The median class is where the cumulative frequency exceeds
`\((51)/(2) = 25.5\)`. In this case, it is the class with the age 17.

Now, use the formula for the median:

`\[ \text{Median} = L + ((51)/(2) - F)/(f) \]`

Here, L is 16 (the lower class boundary of the median class), N is 51 (the total number of observations), F is the cumulative frequency before the median class (i.e., the cumulative frequency of the class with age 16), and f is the frequency of the median class (12).

`\[ \text{Median} = 16 + ((51)/(2) - 10)/(12) \]`

`\[ \text{Median} = 16 + (25.5 - 10)/(12) \]`

`\[ \text{Median} = 16 + (15.5)/(12) \]`

`\[ \text{Median} \approx 17.29 \]`

Mode:

The mode is the value (or values) that appears most frequently. From the given distribution, the age 17 has the highest frequency (12). Therefore, the mode is 17.