List of top Mathematics Questions on Mean, median, mode and standard deviation

Match the following List-I with List-II.

\[ \begin{array}{|c|l|c|l|} \hline \text{List-I} & & \text{List-II} & \\ \hline (a) & \text{Mean} & (i) & \text{List of individual values} \\ \hline (b) & \text{Median} & (ii) & \text{Value appears most often} \\ \hline (c) & \text{Mode} & (iii) & \text{Average for complete data} \\ \hline (d) & \text{Frequency Distribution} & (iv) & \text{Location average} \\ \hline \end{array} \]

The following table shows the number of working hours and the number of employees employed in a small-scale industry. 

\[ \begin{array}{|c|c|} \hline \text{Number of Working Hours} & \text{Number of Employees} \\ \hline 3-5 & 7 \\ \hline 5-7 & 10 \\ \hline 7-9 & 16 \\ \hline 9-11 & 47 \\ \hline 11-13 & 12 \\ \hline 13-15 & 8 \\ \hline \text{Total} & 100 \\ \hline \end{array} \]

Statements:

(i) Average number of working hours of employees is 9.42 hours. 
(ii) The number of workers working less than nine hours is 33. 
(iii) The number of workers working more than average working hours is 67.

For a symmetrical distribution:
The standard deviation of a distribution is 5. If each observation is increased by 2, then the new standard deviation will be:
If the mode of a distribution is 18 and the mean is 24, then the median is:
The relation between mean, median and mode for a moderately asymmetrical distribution is:
The average of squared deviations from mean is called:
The algebraic sum of the deviations of a set of \(n\) values from their arithmetic mean is:

If the mean of the distribution is \(5\), then the value of \(P\) is:

\[ \begin{array}{|c|c|c|c|c|c|} \hline x_i & 2 & 4 & 6 & P & 10 \\ \hline f_i & 3 & 2 & 1 & 4 & 2 \\ \hline \end{array} \]
 

Find the Mean and Median of the data \[ 11,\ 7,\ 6,\ 9,\ 12,\ 15,\ 19,\ 20 \]
Consider the following statements:
• [(i)] If you add 9 to each entry that adds 9 to the average.
• [(ii)] If you add 9 to each entry that adds 9 to the standard deviation.
• [(iii)] If you double each entry on a list that doubles the average.
• [(iv)] If you double each entry on a list that doubles the standard deviation. Which of the following is correct?

Calculate the mean (expected value) of a random variable \( X \) given its probability distribution setup below: 

\( X \)123
\( P(X) \)\( 0.2 \)\( 0.5 \)\( 0.3 \)
A survey conducted on 20 households in a locality resulted in the following frequency table. The mode of the data is:
The mode of the data \(5,\ 7,\ 9,\ 7,\ 11,\ 13,\ 7,\ 15,\ 17,\ 19\) is:
The value which occurs most frequently in a data set is called:

Find the mean and mode of the following data:

Class15--2020--2525--3030--3535--4040--45
Frequency1210151175
Mean, Median and Mode of a data are related by the relation