A researcher wants to conduct a study to find out if there is a correlation between the analytical skills of adults with age. The researcher invited 80 adults to solve a number puzzle. The cumulative frequency curve shows the distribution of the time taken.

(a)
Use the curve to estimate
1. ((i))
  the median time taken,
  
  Answer ... s
2. ((ii))
  the interquartile range of the time taken.
  
  Answer ... s
(b)
20% of the adults took more than n seconds to solve the puzzle.

Find n.
1. Answer n = ...
(c)
The frequency distribution of the data for the 80 adults invited to solve the number puzzle is shown in the table.

Find an estimate of the standard deviation of the time taken by the 80 adults to solve the number puzzle.

Answer ... s
(d)
The same group of adults were each given a word puzzle to solve.

The box-and-whisker plot shows the distribution of the time taken.

Make two comparisons between the performances of the adults in solving the two puzzles.

Answer

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

1. Find the class midpoints and calculate the estimated mean.

Use midpoints $10, 30, 50, 70$ for the four classes.

$\sum fx=5(10)+40(30)+29(50)+6(70)=3120$

$\bar{x}=\frac{3120}{80}=39$

2. Apply the grouped-data standard deviation formula.

$\sum fx^2=5(10^2)+40(30^2)+29(50^2)+6(70^2)$

$=500+36000+72500+29400=138400$

$\text{standard deviation}=\sqrt{\frac{\sum fx^2}{\sum f}-\bar{x}^2}$

$=\sqrt{\frac{138400}{80}-39^2}$

$=\sqrt{1730-1521}$

$=\sqrt{209}=14.456\ldots$

Answer

$15.7$ s

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.