The following grouped data show the ages (in years) of 70 participants in a survey.

Class interval | Frequency
0-9 | 5
10-19 | 8
20-29 | 12
30-39 | 15
40-49 | 10
50-59 | 4
60-69 | 6

(a) Identify the modal class.
(b) Estimate the mode using the formula $ \text{Mode} = L + \frac{f_m - f_{m-1}}{(f_m - f_{m-1}) + (f_m - f_{m+1})} \times w $, where $L$ is the lower limit of the modal class, $f_m$ its frequency, $f_{m-1}$ and $f_{m+1}$ the frequencies of the adjacent classes, and $w$ the class width.
(c) Using the assumed‑mean method with an assumed mean $A = 35$ and step size $h = 10$, estimate the mean of the data.
(d) What percentage of participants are estimated to be older than the mean?

Question

The following grouped data show the ages (in years) of 70 participants in a survey.

Class interval | Frequency
0-9 | 5
10-19 | 8
20-29 | 12
30-39 | 15
40-49 | 10
50-59 | 4
60-69 | 6

(a) Identify the modal class.
(b) Estimate the mode using the formula $ \text{Mode} = L + \frac{f_m - f_{m-1}}{(f_m - f_{m-1}) + (f_m - f_{m+1})} \times w $, where $L$ is the lower limit of the modal class, $f_m$ its frequency, $f_{m-1}$ and $f_{m+1}$ the frequencies of the adjacent classes, and $w$ the class width.
(c) Using the assumed‑mean method with an assumed mean $A = 35$ and step size $h = 10$, estimate the mean of the data.
(d) What percentage of participants are estimated to be older than the mean?

Accepted Answer

Modal class: 30-39; Mode ≈ 33.75 years; Estimated mean ≈ 33.57 years; About 40.2 % of participants are older than the mean.

Neco 2018 Data Processing Question 42

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