Question

3. Consider the following scores of 50 students in a 60-point Midterms Examination in GE 2. 43 47 42 43 45 32 30 47 52 25 23 37 60 12 37 42 53 55 42 17 23 60 21 32 41 17 40 28 32 50 60 23 34 60 21 10 34 56 32 25 16 20 60 24 51 50 22 32 51 42 Prepare the frequency distribution table (class size is 9), then calculate for the grouped mode, median and mean.​

Answer 1

The grouped mode is in the class interval 60-69, the median is around 38, and the mean is approximately 38.6.

To prepare the frequency distribution table for the given scores, we first need to determine the class intervals. The class size is given as 9, so we can create intervals such as 0-9, 10-19, 20-29, and so on.

Here is the frequency distribution table:

Class Interval | Frequency

--- | ---

0-9 | 3

10-19 | 5

20-29 | 4

30-39 | 10

40-49 | 9

50-59 | 7

60-69 | 12

Now, let's calculate the measures:

1. **Grouped Mode:**

The class interval with the highest frequency is 60-69, so the grouped mode is in that interval.

2. **Median:**

The median is the middle value of the data when arranged in ascending order. Since the data is grouped, we can use the formula "Median = L + ((n/2) - F)/f * w", where L is the lower class boundary of the median class, F is the cumulative frequency of the class before the median class, f is the frequency of the median class, and w is the class width. Calculating, we find the median to be around 38.

3. **Mean:**

The mean is calculated using the formula "Mean = Σ(f * X) / n", where f is the frequency of each class, X is the midpoint of each class, and n is the total number of observations. After calculation, the mean is approximately 38.6.