6, 9, 15, x + 4, x + 8, x + 12, 30, 32
The problem asks us to find the value of x given a dataset arranged in ascending order and its median.
Understanding Median Calculation
The dataset provided is: 6, 9, 15, x + 4, x + 8, x + 12, 30, 32. There are 8 observations in total (n=8). Since 'n' is an even number, the median is calculated as the average of the two middle observations.
- The middle positions are the $\frac{n}{2}$th and $(\frac{n}{2} + 1)$th observations.
- For n=8, these are the $\frac{8}{2} = 4$th and $(\frac{8}{2} + 1) = 5$th observations.
Calculating the Value of x
The 4th observation is x + 4 and the 5th observation is x + 8. The median is given as 19.
Using the median formula:
$ \text{Median} = \frac{(\text{4th observation}) + (\text{5th observation})}{2} $Substitute the values:
$ 19 = \frac{(x + 4) + (x + 8)}{2} $Now, solve for x:
- Simplify the numerator: $19 = \frac{2x + 12}{2}$
- Multiply both sides by 2: $19 \times 2 = 2x + 12$
- $38 = 2x + 12$
- Subtract 12 from both sides: $38 - 12 = 2x$
- $26 = 2x$
- Divide by 2: $x = \frac{26}{2}$
- $x = 13$
Therefore, the value of x is 13.
Verification
If x=13, the data becomes: 6, 9, 15, (13+4), (13+8), (13+12), 30, 32, which is 6, 9, 15, 17, 21, 25, 30, 32. The median is $\frac{17 + 21}{2} = \frac{38}{2} = 19$. This confirms our result.
Similar Questions
- The marks scored by 10 students are given below.
17, 19, 12, 20, 19, 14, 15, 18, 19, 14
The mode of the given data is: - Let a set S = {1, 2, 2, 3, 3, 3, 4, 4, 4, 4}. Then the value of $4 \times \text{mean} + 2 \times \text{mode} - 8 \times \text{median}$ is:
- The weights (in kg) of 7 men are 64, 63, 62, 65, 67, 66 and 61. The median weight is:
- Which of the following CANNOT take a negative value?
- The given data is arranged in ascending order and its median is 17. Find the value of $x$.
$8, 10, 12, 15, x, x + 2, 20, 25, 30, 32$ - Find the sum of the mean, median and mode of the given data.
$9, 35, 20, 25, 25, 15, 25$ - In the given data if 30 is replaced by 100 then find the difference of the two medians.
80, 90, 40, 30, 20, 10, 70, 60, 50 - Find the mean height of persons from the following data.
Height (cm) Number of persons 120 3 130 4 140 5 150 6 160 2 - If the mean of the following data is k, then find the value of k.
Value 3 2 k 4 5 Frequency k 2k 3k 4k 5k - A alone can complete a work in 12 days and B alone can complete the same work in 18 days. They started working together, but A left after 3 days. In how many days will B alone be able to complete the remaining work?
Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
