Understanding
Q15
Answer the following questions.
a. Add one more number to the set of data $3,4,4,6$ so that the mean of the new set is equal to its median.
The number is
SUBMIT ANSWER
$1 \operatorname{mark}(\mathrm{s})$
12.3 MEASURES OF SPREAD
Answer
\(\boxed{\text{The number to add to the set is }\frac{14}{3}}\)
Step 1 ：Calculate the mean and median of the current set: \(data = [3, 4, 4, 6]\), \(mean = 4.25\), \(median = 4.0\)
Step 2 ：Let x be the number we need to add to the set. The new mean will be \((sum\ of\ the\ set + x) / 5\) and the new median will be the middle number of the sorted set.
Step 3 ：Set up an equation and solve for x: \(\frac{x}{5} + \frac{17}{5} = \frac{x}{2} + 2\)
Step 4 ：Solve for x: \(x = \frac{14}{3}\)
Step 5 ：\(\boxed{\text{The number to add to the set is }\frac{14}{3}}\)
