Important Questions: Statistics - Year 10 MCQ

• When computing the mean of grouped data, we assume that the frequencies are centered at the class marks of the classes.
• This means that each frequency is associated with the midpoint of its respective class interval.
• Using the class marks allows for an accurate calculation of the mean by multiplying each class mark by its frequency, summing these products, and then dividing by the total frequency.

The correct answer is b

   A cumulative frequency table helps to determine the median of the series.

Sum of 100 observations = 100 x 49 = 4900
Correct sum = 4900 - [40 + 20 + 50] + [60 + 70 + 80] = 5000
∴ Correct mean = 5000/100 = 50

The formula to find the mode of the grouped data is: Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h. Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class proceeding to modal class, f₂ = frequency of class succeeding to modal class.

As per the given question,

X_mean = ∑f_i x_i /∑f_i

7.5 = (120+3k)/30

225 = 120+3k

3k = 225-120

3k= 105

k=35