NIMCET 2026
An investigator has missed a value while collecting data in an experiment. Denoting the missing value by , the observations are: 10, 4, 11, 6, 17, 15, 9, 8, . What should be the value of , if he wants mean = median = mode for this data set?
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option B — 10
Detailed Solution
Sum of known values , so mean .
The 8 known values are all different, so the mode can only exist if repeats one of them; then mode .
Mean :
Check the median with : sorted 4, 6, 8, 9, 10, 10, 11, 15, 17 → 5th value = 10. Mean = 10, median = 10, mode = 10.
Quick tip
Mode must equal ; solve mean
💬 Discussions on this question
Ask a doubt ›Still stuck on this question? Ask our faculty and fellow students — answers appear here.
Ask a doubtMore Statistics Questions
View all ›- Q1.The distances in metres for seven throws of a shot-putter are: 14.5, 15.2, 16.8, 17.1, 15.9, 16.3, 14.7. Calculate the sample mean and sample standard deviation. Round to two decimals.
- Q2.Consider the following grouped data. Find the mode. Class interval: 20–25, 25–30, 30–35, 35–40, 40–45, 45–50 Number of students: 8, 14, 20, 18, 10, 6
- Q3.For a given sample, the computed values of the variance and fourth central moment are 3 and 63 respectively. Then the underlying frequency distribution is classified as:
- Q4.The mean of 5 observations is 5 and their variance is 12.4. If three of the observations are 1, 2 and 6, then the mean deviation from the mean of the data is:
- Q5.For a group of 100 candidates, the mean and standard deviation of scores were found to be 40 and 15 respectively. Later on, it was found that the scores 25 and 35 were misread as 52 and 53 respectively. Then the corrected mean and standard deviation are
More Quantitative Aptitude Questions
- Q1.By selling 45 lemons for ₹40, a man loses 20%. How many lemons should he sell for ₹24 to gain 20%?Profit, Loss & Discount
- Q2.The marked price of an article is 1.45 times its cost price. Its selling price is ₹1,500 and the profit is 25%. What is the discount percentage? Profit, Loss & Discount
- Q3.Let A be a real number. Then the roots of the equation are real and distinct if and only if Quadratic Equations
- Q4.The number of distinct real roots of the equation is Quadratic Equations
- Q5.The roots of are:Quadratic Equations
Statistics — Preparation
This question tests your understanding of Statistics, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Statistics deals with collecting, summarising and interpreting data. This topic covers measures of central tendency (mean, median and mode) for ungrouped and grouped data, and measures of dispersion such as range, mean deviation, variance, standard deviation and the coefficient of variation. Exam questions test calculating these measures, the effect of adding or multiplying every observation by a constant, combined mean and variance of two groups, and comparing the consistency of two data sets. Remember that adding a constant to every value changes the mean but not the variance or standard deviation, while multiplying by k multiplies the standard deviation by |k|. Facts like these solve many questions without any calculation. Practise the statistics questions below, each with a step-by-step solution.