Statistics – important questions for Boards 2027
CBSE Class 10 Maths
Which of the following lists the measures of central tendency studied in statistics? (A) Mean, median and mode (B) Range, area and volume (C) Ogives, axes and scales (D) Frequency, class mark and interval.
Answer
(A) Mean, median and mode — these are measures of central tendency.
Write the formula for the class mark of an interval with lower limit L and upper limit U.
Answer
The class mark represents the observations in an interval. It is the average of the upper and lower class limits: class mark = (U + L) ÷ 2.
In a frequency distribution, what does the frequency fᵢ corresponding to an observation xᵢ tell you?
Answer
1. The frequency fᵢ corresponding to observation xᵢ tells how many times that value occurs in the data. If fᵢ is zero, the observation does not occur. 2. The frequencies for all observations add up to the total number of observations. In calculating the mean, fᵢxᵢ gives the total contribution of all occurrences of xᵢ.
Write the grouped-data median formula and explain the meanings of l, n, cf, f and h in it.
Answer
The median of grouped data is the value within the median class that divides the distribution into two halves. 1. Formula — Median = l + ((n/2 − cf)/f) × h. The formula estimates the median using the median class and its cumulative frequency. 2. Lower limit and total — l is the lower limit of the median class, and n is the total number of observations in the distribution. The value n/2 represents half the total number of observations. 3. Cumulative frequency and frequency — cf is the cumulative frequency of the class preceding the median class, and f is the frequency of the median class. The difference n/2 − cf gives the position of the median within that class. 4. Class size — h is the class size, assuming equal class sizes. The median class is the class whose cumulative frequency is greater than and nearest to n/2. The formula locates the median within the interval containing the middle observation.
For observations xᵢ with corresponding frequencies fᵢ, explain how the mean is calculated and state the formula using sigma notation.
Answer
The mean of a frequency distribution is the average value of its observations. 1. Each observation xᵢ occurs fᵢ times, so the total contribution of all its occurrences is fᵢxᵢ. 2. Adding these contributions for all observations gives the total sum, Σfᵢxᵢ, while adding their frequencies gives the total number of observations, Σfᵢ. 3. Divide the total sum of observations by the total number of observations. The formula is x̄ = Σfᵢxᵢ / Σfᵢ. 4. For grouped data, each class interval is represented by its class mark xᵢ, found by averaging its upper and lower class limits. This uses the assumption that the frequency is centred around the class midpoint. Thus, the formula gives the exact mean for ungrouped data; for grouped data, the midpoint assumption makes the mean approximate.
Explain how class marks represent the observations in a grouped frequency distribution. Then describe the direct, assumed-mean and step-deviation methods for finding the grouped mean, giving the formula used in each method and explaining how the choice of assumed mean affects the result.
Answer locked. Unlock all answers on SmartKalike
Which term describes the running total of frequencies in a distribution? (A) Class mark (B) Cumulative frequency (C) Modal class (D) Frequency polygon.
Answer locked. Unlock all answers on SmartKalike
Define the mode of a set of observations in terms of frequency.
Answer locked. Unlock all answers on SmartKalike
For ungrouped observations arranged in ascending order, explain how to find the median when the number of observations is (i) odd and (ii) even.
Answer locked. Unlock all answers on SmartKalike
Before using the grouped-data median formula, what condition must the class intervals satisfy? Explain why this condition is necessary, using the intervals 10–19 and 20–29 as an example.
Answer locked. Unlock all answers on SmartKalike
9 more probable questions in this chapter, every one with a full answer.
Unlock all answers on SmartKalike