Statistics

In a distribution, if the mean is $15$ and the median is $15$, the mode is likely to be:

Find the mean of the squares of the first three natural numbers.

Which observation divides the data into two equal parts when arranged in order?

If $3 \times Median = 40$ and $2 \times Mean = 30$, find the $Mode$.

If the median of $10, 12, 15, x, 19, 21$ (arranged in order) is $16.5$, find $x$.

For the data set $2, 2, 4, 5, 5$, which of the following is true?

In the frequency distribution, the class with the highest frequency is called the:

The following frequency distribution: $0-10$ (5), $10-20$ (8), $20-30$ (7), $30-40$ (10), $40-50$ (20). Calculate the median class lower limit.

The mean of $n$ observations $x_1, x_2, \dots, x_n$ is $\bar{x}$. What is the value of $\sum_{i=1}^{n} (x_i - \bar{x})$?

In a distribution with unequal class intervals, for finding the mode, we must first:

A kink (zigzag line) is used on the horizontal axis of a histogram when:

In a histogram, if the class intervals are $0-10, 10-20, 20-30$, what is the class mark of the second class?

Which graphical representation is specifically used to find the Mode of a grouped frequency distribution?

The point of intersection of the 'Less than' ogive and the 'More than' ogive for a data set gives the value of the:

Which of the following is NOT required to draw a frequency polygon?

In a distribution, the 'less than' ogive and 'more than' ogive intersect at $(35, 42)$. What is the total frequency $N$ of the distribution?

How many students scored more than 60 marks according to the given 'More than' Ogive?

In the graphical representation of a continuous frequency distribution, the midpoints of the classes are $(12, 22, 32, 42, 52)$. If these points are used to draw a frequency polygon, what is the width of each class interval?

A cumulative frequency curve is used to find the 60th percentile of a distribution of 250 workers' wages. Which y-coordinate value on the ogive corresponds to this percentile?

While constructing a histogram for a grouped frequency distribution, the 'kink' (zigzag line) on the x-axis is used between the origin and the first class. What is the primary reason for using this kink?

The semi-interquartile range is calculated by dividing the interquartile range by:

If $Q_1 = 100$ and the semi-interquartile range is $50$, find $Q_3$.

Calculate the semi-interquartile range for the data: $5, 5, 15, 15$.

In an ogive with total frequency $N=120$, the median corresponds to the value on the x-axis where the y-axis is:

If the range of a symmetric distribution is $100$, and the quartiles are $Q_1=40, Q_3=80$, what is the Semi-Interquartile Range?

Find the $IQR$ for the data: $1.2, 2.5, 3.8, 4.1, 5.6, 6.7, 7.9, 8.2$.

In a distribution of 25 students, the Lower Quartile corresponds to the:

In a cumulative frequency curve (ogive), if the total frequency is 500, the upper quartile is the value of the variable corresponding to the cumulative frequency of:

The upper quartile of a distribution is 50. If the interquartile range is 20, what is the value of the lower quartile?

The interquartile range of a set of 5 numbers is 10. If the numbers are $x, x+5, x+10, x+15, x+20$, find the $IQR$ using the $(n+1)/4$ and $3(n+1)/4$ terms.