Statistics

Find the total frequency for the data: $10-20$ (5), $20-30$ (12), $30-40$ (3).

What is the lower limit of the class $250 - 300$?

If $x_i = 50$ and $d_i = 10$, find the assumed mean $a$.

Find the class mark for the class $40 - 60$.

If the assumed mean is $a$, the mean of grouped data is $\bar{x}$, and $h$ is class size, what is the value of $\frac{\sum f_i d_i}{\sum f_i}$ if we use the step deviation method notation $d_i = x_i - a$?

Find the mean of the data where classes are $0-4, 4-8, 8-12, 12-16$ and frequencies are $2, 4, 3, 1$.

Calculate the mean: Classes $0-10, 10-20, 20-30, 30-40, 40-50$ with frequencies $5, 10, 20, 10, 5$.

If the class mark of a class is $25$ and the class width is $10$, the class interval is:

The difference between the mean calculated by the Direct Method and the Assumed Mean Method for the same grouped data is:

If the mean of $10$ observations is $x$ and the mean of another $15$ observations is $y$, the mean of the combined $25$ observations is:

When calculating median for grouped data, the classes must be:

If $n=30$, $cf$ of the class preceding the median class is 12, $f$ of the median class is 6, $l=20$, and $h=5$, the median is:

If the median class is 0-10, what is the value of $l$?

In the median formula, what is the purpose of the term $\left( \frac{\frac{n}{2} - cf}{f} \right) \times h$?

What is the class mark of the median class for the data: $0-10(4), 10-20(7), 20-30(10), 30-40(8), 40-50(1)$?

If a data set has classes $0-5, 5-10, 10-15, 15-20$ with frequencies $2, 3, 5, 4$, what is the cumulative frequency of the median class?

For a distribution, if $l=10, n=50, cf=12, f=20, h=5$, find the median.

In the formula for Median, what is the value of $(n/2 - cf)$ if the median is 50, $l=40, h=20, f=10$?

The median of a distribution is 525. The total frequency is 100. If the cumulative frequency before the median class $500-600$ is $36+x$ and the frequency of the median class is 20, find $x$.

If the median of a continuous frequency distribution is 24 and the median class is $20-30$ with frequency 20 and $cf$ of the preceding class is 10, find the class size $h$ if $n=70$.

Identify $h$ for the data: $20-30, 30-40, 40-50$.

In the mode formula, if $f_0$ and $f_2$ are both zero, the mode becomes:

If class intervals are $0-100, 100-200, 200-300$ with frequencies $40, 60, 30$, identify the modal class.

The value of the mode is always _____ the lower limit of the modal class if $f_1 > f_0$.

Find the mode: Class $10-25$ (2), $25-40$ (3), $40-55$ (7), $55-70$ (6), $70-85$ (6).

What is the mode of a distribution where all frequencies are equal?

In the mode formula, if $2f_1 - f_0 - f_2$ is denoted by $D$, and $f_1 - f_0$ is $4$, $h=10$, $l=20$, $Mode=25$, find $D$.

Find the mode: Class $1-5 (2), 6-10 (4), 11-15 (8), 16-20 (3)$.

Mode of a distribution is 75. Modal class is $70-80$. $f_1=25, f_2=15$. Find $f_0$.

The mode of the distribution $0-50 (10), 50-100 (15), 100-150 (30), 150-200 (20), 200-250 (15)$ is:

In the formula for median, $cf$ stands for the cumulative frequency of the class:

Find the mean of the first five odd natural numbers.

In the 'more than' type ogive, the cumulative frequencies are plotted against the:

Which measure of central tendency is the most used because it takes all observations into account?

Consider the following 'less than' cumulative frequency distribution:

• Less than $10$: $4$
• Less than $20$: $12$
• Less than $30$: $30$
• Less than $40$: $45$

Based on this data, find the class mark of the modal class.

In a grouped frequency distribution, the total number of observations is $80$ and the cumulative frequency of the class preceding the median class is $32$. If the median class is $150-160$ and its frequency is $16$, calculate the median of the distribution.

If the median of the observations $x/5, x, x/4, x/2, x/3$ (where $x > 0$) is 8, find the value of $x$.

If for a given data, $\sum f_i = 100$ and $\sum f_i x_i = 1250 + 25k$, and the mean is 15, calculate $k$.

Which measure of central tendency is most affected by extreme values (outliers)?

If the class intervals are $10-20, 20-30, 30-40, 40-50$, the class marks are $x_i$. If we define $d_i = x_i - 35$, which value was chosen as the assumed mean?

If $\sum f_i u_i = -10$, $\sum f_i = 50$, $a = 100$, and $h = 10$, then the mean $\bar{x}$ is:

If $x_i$ is the class mark and $f_i$ is the frequency, the mean $\bar{x}$ is defined as:

The class mark of the interval $a - b$ is:

If the class size is $8$ and the upper limit is $32$, the lower limit is:

If the class mark of a class is $42$ and the class size is $10$, what are the lower and upper limits of the class?

Find the mean of the data: Class $0-50 (10), 50-100 (15), 100-150 (30), 150-200 (25), 200-250 (20)$.

If the mean of $0-10, 10-20, 20-30$ with frequencies $2, 3, 5$ is $23$, find $\sum f_i x_i$.

Two groups of sizes $40$ and $60$ have means $10$ and $15$ respectively. What is the mean of the combined group of $100$ observations?

If the class marks of a grouped data are $5, 15, 25, 35$ and the mean is $22$, and $\sum f_i = 20$, find the value of $\sum f_i x_i$.

Calculate the mean of the following frequency distribution: $0-10 (7), 10-20 (8), 20-30 (12), 30-40 (13), 40-50 (10)$.

If the modal class is $15-25$, the upper limit is:

If $f_1 = 15, f_0 = 5, f_2 = 5$, find the value of $(2f_1 - f_0 - f_2)$.

What is the lower limit of the modal class for the table: $0-20$ (5), $20-40$ (12), $40-60$ (7)?

If Mean $= 30$ and Median $= 30$, find Mode.

If the difference between mode and median of a data is $24$, then the difference between median and mean is:

Calculate the mode: $l=20, f_1=12, f_0=8, f_2=8, h=10$.

For a distribution, $Mode = 35.5$. If the modal class is $30-40$ and $h=10, f_1=30, f_0=15$. Find $f_2$.

The difference between the lower limit of the modal class and the mode of a distribution is $5$. If $h=10, f_1=20, f_0=10$, find $f_2$.

For a distribution, modal class is $30-40$, $f_1=10, f_0=8, f_2=9$. Find the mode.

If the mean is $x$ and the mode is $y$, then according to the empirical formula, the median is:

The construction of a cumulative frequency table is useful in determining the:

If the median of a data is $45$ and the median class is $40-50$, what is the value of $l$?

In the formula for median, if $n=100, cf=40, f=10, l=50, h=10$, what is the value of the term $\frac{n/2 - cf}{f}$?

If the class interval is $10-20$, what is the upper limit?

If the intersection point of two ogives is ($x, y$), then the median is given by:

If the median class is 40-50, the cumulative frequency of the class preceding it is 25, the frequency of the median class is 15, and $n=80$, find the median.

What is the median of the following frequency distribution? Class 0-6 (f=4), 6-12 (f=8), 12-18 (f=3).

Which of the following is true for the median class in any frequency distribution?

If the sum of the frequencies of a distribution is 50 and the cumulative frequency of the class before the median class is 20, while the frequency of the median class is 10, with $l=40, h=10$, find the median.

Given the distribution: $0-100 (2), 100-200 (5), 200-300 (9), 300-400 (12), 400-500 (17), 500-600 (20)$. What is the cumulative frequency of the class $400-500$?