Statistics

Find the mean of the data: $4, 6, 8, 10, 12.

Find the median of: $3, 6, 10, 14, 18.

Find the median of: $5, 8, 12, 15.

Find the mode of: $5, 7, 7, 8, 9, 7, 10.

Find the range of: $14, 22, 8, 18, 25, 10.

Find the mean of: $6, 9, 12, 15, 18.

Find the mode and the range of: $7, 7, 9, 10, 14.

A boxplot has lower quartile 12, median 18, and upper quartile 24. State (a) the IQR and (b) the median.

A stem-and-leaf plot shows $1\,|\,2\;5\;9$ and $2\,|\,1\;4\;6\;7$. How many values are there?

In a frequency table, value $x$ has frequency 2; value 3 has frequency 5; value 5 has frequency 3. Total frequency 10. Mean: $x = ?$ given mean is 4. (Find $x$.)

Find the mean of: $1(4), 3(3), 5(3) (where format is "value(frequency)").

A data set has 25 values. What is the median position?

For the ordered data $3, 5, 8, 9, 11, 13, 15, 17, 20, find $Q_1$ and $Q_3$.

A data set has $Q_1 = 22$ and $Q_3 = 41$. Find the IQR.

For the data $2, 4, 5, 7, 9, 11, 12, 15, 18, find min, $Q_1$, median, $Q_3$, max.

Two boxplots are shown. Boxplot A: median 18, IQR 10. Boxplot B: median 22, IQR 6. Which group has more consistent values?

A test was sat by 20 students. Scores: 1(2), 2(5), 3(8), 4(3), 5(2). Find the mean.

From the frequency table, state the modal value: 1(4), 2(7), 3(10), 4(5), 5(4).

A data set $\{3, 5, 7, x, 11\}$ has mean $8$. Find $x$.

A boxplot has whiskers from 0 to 50, $Q_1 = 10$, median 15, $Q_3 = 22$. Is the distribution symmetric or skewed?

A cumulative frequency curve for 100 students has cf = 25 at score 12, cf = 50 at score 18, cf = 75 at score 23. State $Q_1$, median, $Q_3$.

For the cumulative frequency data: $Q_1 = 25$, $Q_3 = 48$. Find the IQR.

A grouped frequency table has: $[0, 10)$ freq 4; $[10, 20)$ freq 8; $[20, 30)$ freq 6; $[30, 40)$ freq 2. Estimate the mean.

A boxplot has $Q_1 = 20$, $Q_3 = 40$. Using the 1.5×IQR rule, determine if 75 is an outlier.

Group A has median 25, IQR 10. Group B has median 25, IQR 20. Compare the spreads.

From the cumulative frequency curve: at score = 30, cf = 75; at score = 40, cf = 95. How many students scored between 30 and 40?

A grouped table has total frequency 60, with cumulative frequencies at class boundaries: 8, 22, 45, 60. The median is in which class?

A data set has values 1, 2, 3, 4 with frequencies 4, $x$, 6, 3. The mean is 2.5. Find $x$.

A boxplot shows min 5, $Q_1$ 12, median 20, $Q_3$ 28, max 35. What percentage of data lies above $Q_3$?

A data set has $n = 40$ values with mean $22.5$. Find the sum.

Class A has 25 students with mean test score 60. Class B has 15 students with mean 72. Find the combined mean.

Six values are $\{12, 15, 17, x, 22, 25\}$. The median is 19. Find $x$.

A cumulative frequency table on 200 values shows cf = 80 at score 50, cf = 120 at score 70. Estimate the score for the 60th percentile.

Group A: min 5, $Q_1$ 12, median 18, $Q_3$ 25, max 35. Group B: min 8, $Q_1$ 18, median 22, $Q_3$ 28, max 38. Make two comparisons.

A data set has $Q_1 = 15$, $Q_3 = 35$. Identify values from $\{3, 10, 22, 50, 70\}$ that are outliers.

In a test, the mean of 20 students is 72. After re-marking, two scores increased by 5 each. What is the new mean?

Grouped data: $[0, 10)$ freq 5; $[10, 20)$ freq 12; $[20, 30)$ freq 8; $[30, 50)$ freq 5. State the modal class and explain why frequency density matters here.

Two data sets both have mean 10. Set A has range 4; Set B has range 20. Which is more spread out?

A class of $19$ students has mean test score $70$. A new student joins with score $50$. Find the new mean (1 d.p.).

Five integers have mean 5, median 5, and mode 7. State a possible set of integers.