Manipur Board Solutions for Chapter: Statistics, Exercise 1: EXERCISE 14.1

State a common experience in which you collect the data to get an information.

The performance given in grades of $45$ students of a class are as follows:
$({\mathrm{A}}^{+}, \mathrm{A}, {\mathrm{B}}^{+}, \mathrm{B}, {\mathrm{C}}^{+}, \mathrm{C} \mathrm{and} \mathrm{D}$ are $7$ grades$)$

$$\begin{gathered} \mathrm{A}, \mathrm{B}, {\mathrm{C}}^{+}, \mathrm{C}, \mathrm{C}, \mathrm{D}, {\mathrm{A}}^{+}, \mathrm{B}, {\mathrm{B}}^{+}, \mathrm{B}, {\mathrm{B}}^{+}, \mathrm{C}, {\mathrm{C}}^{+}, \mathrm{D}, {\mathrm{A}}^{+} \\ {\mathrm{B}}^{+}, \mathrm{A}, {\mathrm{A}}^{+}, \mathrm{C}, {\mathrm{C}}^{+}, \mathrm{A}, \mathrm{B}, {\mathrm{B}}^{+}, \mathrm{C}, \mathrm{D}, {\mathrm{A}}^{+}, \mathrm{B}, {\mathrm{B}}^{+}, {\mathrm{B}}^{+}, \mathrm{C} \\ \mathrm{B}, {\mathrm{B}}^{+}, \mathrm{B}, {\mathrm{B}}^{+}, {\mathrm{A}}^{+}, \mathrm{C}, \mathrm{C}, {\mathrm{C}}^{+}, \mathrm{A}, {\mathrm{A}}^{+}, \mathrm{B}, {\mathrm{B}}^{+}, {\mathrm{B}}^{+}, \mathrm{C}, \mathrm{A} \end{gathered}$$

Construct a frequency distribution to represent the data. Determines the grades which are obtained by maximum and minimum number of students. Find also the median grade. Which one of the measures of central tendency is not determinable for this non-numerical data.

What are the mean and median of the first eleven natural numbers? Can you estimate the mode? If so what is it?

The following are the weight in $\mathrm{kg}$ of $20$ pupils in a class:
$$\begin{gathered} 30, 37, 45, 32, 26, 40, 26, 31, 30, 35, \\ 28, 32, 35, 41, 28, 27, 42, 36, 32, 36 \end{gathered}$$

Using tally marks form an ungrouped frequency table thereby showing the frequency and cumulative frequency columns. Also find three measures of central tendency of the data.

The following are the weight in $\mathrm{kg}$ of $20$ potatoes in a farm:
$$\begin{gathered} 30, 37, 45, 32, 26, 40, 26, 31, 30, 35, \\ 28, 32, 35, 41, 28, 27, 42, 36, 32, 36 \end{gathered}$$

Taking two as width if each class construct a continuous grouped frequency distribution table. Also show the mid-values of the classes and the cumulative frequencies.

For a certain locality, the data of monthly household consumption of electricity measured in units of energy is given below:

The monthly rate of tax is divided into two categories:
Category$-\mathrm{I}$: $₹3$ per unit for households coming $50$ units or less.
Category$-\mathrm{II}:$ $₹1$ for every additional unit of energy above $50$ units.

Find the number of consumers paying the first and second categories of taxes.

The following is the survey report of the weekly income of the families of a ward of a municipality:

From the above data construct a continuos frequency table and also find the cumulative frequency of each class. Further find the number of families whose weekly income is at the most $₹1000$.