NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 13: Statistics and Probability

Exercise 13.2

The median of an ungrouped data and the median calculated when the same data is grouped are always the same. Do you think that this is a correct statement? Give reason.

In calculating the mean of grouped data, grouped in classes of equal width, we may use the formula

\[ \bar{x} = a + \dfrac{f_i d_i}{f_i} \]

where a is the assumed mean. a must be one of the mid–points of the classes. Is this correct? Justify your answer.

Is it true to say that the mean, mode and median of grouped data will always be different? Justify your answer.

Will the median class and modal class of grouped data always be different? Justify your answer.

In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is \(\dfrac{1}{4}\). Is this correct? Justify your answer.

A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3) . Are the outcomes 1, 2 and 3 equally likely to occur? Give reasons.

Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36? Why?

When we toss a coin, there are two possible outcomes – Head or Tail. Therefore, the probability of each outcome is \(\dfrac{1}{2}\). Justify your answer.

A student says that if you throw a die, it will show up 1 or not 1. Therefore, the probability of getting 1 and the probability of getting ‘not 1’ each is equal to \(\dfrac{1}{2}\). Is this correct? Give reasons.

I toss three coins together. The possible outcomes are no heads, 1 head, 2 heads and 3 heads. So, I say that probability of no heads is \(\dfrac{1}{4}\). What is wrong with this conclusion?

If you toss a coin 6 times and it comes down heads on each occasion. Can you say that the probability of getting a head is 1? Give reasons.

Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

If I toss a coin 3 times and get head each time, should I expect a tail to have a higher chance in the 4th toss? Give reason in support of your answer.

A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since this situation has only two possible outcomes, so, the probability of each is \(\dfrac{1}{2}\). Justify.