Students were timed as they attempted to perform a simple test of dexterity. The incomplete data of results is shown below. Find x, if the mean time taken was 16 seconds.
Time Taken (s) Frequency
(0 - 10) 20
(10 - 20) 50
(20 - 30) x
My equation:
850x + 25x /16= 70 + x
850 + 24x / 16= 70
850 + 24x = 1120
24x = 270
x = 11.25
Is my equation wrong or did I make a mistake?
i realised what went wrong order of operations x is 30 :)
Upon reviewing your equation, it seems that there is a mistake in your calculation. Let me explain the correct approach for solving this problem.
To find the missing value, x, we need to consider the mean (average) time taken by the students. The mean can be calculated by dividing the sum of all values by the total number of values.
In this case, we have incomplete data for three intervals: (0 - 10), (10 - 20), and (20 - 30). We are given the frequencies for the first two intervals but not for the third one. To calculate x, we need to find the frequency for the third interval.
Let's break down the steps:
Step 1: Calculate the sum of the products of each frequency and the midpoint of its corresponding interval.
First interval: (0 - 10): The midpoint is (0 + 10) / 2 = 5
Product = 20 * 5 = 100
Second interval: (10 - 20): The midpoint is (10 + 20) / 2 = 15
Product = 50 * 15 = 750
Step 2: Calculate the sum of all the products.
Sum = 100 + 750 = 850
Step 3: Calculate the total frequency.
Total frequency = sum of the given frequencies for the first two intervals = 20 + 50 = 70
Step 4: Calculate the mean time taken.
Mean = sum / total frequency = 850 / 70 = 12.14 (rounded to two decimal places)
From the given information, the mean time taken is 16 seconds. Since we need to find the frequency for the third interval, we can set up the equation:
Mean = (sum of all products + x * midpoint of the third interval) / (total frequency + x)
Substituting the known values:
16 = (850 + 15x) / (70 + x)
Step 5: Solve the equation for x.
Multiply both sides by (70 + x):
16 * (70 + x) = 850 + 15x
1120 + 16x = 850 + 15x
Subtract 15x from both sides:
x = 1120 - 850 = 270
Therefore, the correct value of x, representing the frequency for the third interval, is 270.
Hence, your equation and calculations were incorrect, and the correct value of x is 270.