In a mathematics test, the scores obtained by 45 students were recorded as shown in the table below.Score(x)53576265K768283No. of students46679544The score K with frequency of 9 is not given. Given that ∑fd∑f=−0.6 where d=x−68, and using an assumed mean of 68, determine score K.60696865
Question
In a mathematics test, the scores obtained by 45 students were recorded as shown in the table below.Score(x)53576265K768283No. of students46679544The score K with frequency of 9 is not given. Given that ∑fd∑f=−0.6 where d=x−68, and using an assumed mean of 68, determine score K.60696865
Solution
To solve this problem, we need to use the formula given, which is ∑fd/∑f = -0.6, where d = x - 68.
Step 1: Calculate the value of d for each score x.
For x = 53, d = 53 - 68 = -15 For x = 57, d = 57 - 68 = -11 For x = 62, d = 62 - 68 = -6 For x = 65, d = 65 - 68 = -3 For x = K, d = K - 68 For x = 76, d = 76 - 68 = 8 For x = 82, d = 82 - 68 = 14 For x = 83, d = 83 - 68 = 15
Step 2: Multiply each d value by its corresponding frequency f to get fd.
For d = -15, fd = -15 * 4 = -60 For d = -11, fd = -11 * 6 = -66 For d = -6, fd = -6 * 7 = -42 For d = -3, fd = -3 * 9 = -27 For d = K - 68, fd = (K - 68) * 5 For d = 8, fd = 8 * 4 = 32 For d = 14, fd = 14 * 4 = 56 For d = 15, fd = 15 * 4 = 60
Step 3: Sum all the fd values and all the f values.
∑fd = -60 - 66 - 42 - 27 + (K - 68) * 5 + 32 + 56 + 60 ∑f = 4 + 6 + 7 + 9 + 5 + 4 + 4 + 4 = 45
Step 4: Substitute ∑fd and ∑f into the formula and solve for K.
-0.6 = (∑fd) / 45 -0.6 * 45 = ∑fd -27 = -60 - 66 - 42 - 27 + (K - 68) * 5 + 32 + 56 + 60 Solving for K, we get K = 70.
So, the score K is 70.
Similar Questions
Consider the given table for grade 10 students’ scores in a mathematics test, in a certain school.The scores were recorded out of 50.Scores Observations Frequency21 - 25 21, 23, 23, 25, 25 526 - 30 29, 29, 29 331 - 35 32, 33, 34, 35, 35 536 - 40 38, 38, 38, 38, 40, 39, 38, 39, 39, 40 1041 - 45 44, 44, 44, 44, 45, 45 646 - 50 49, 49, 50 3The number of students who obtained more than 60% score isA. 0B. 24C. 27D. 32
The points scored on a test for a sample of 36 students are summarized in the following table.Number of students Score for each student7 9015 8014 70Find the mean points scored. Round your answer to the nearest tenth.points
The mean of the marks scored by 50 students was found to be 39. Later it was found that a score of 43 was written as 23. Find the correct mean.
On Monday a group of students took a test, and the average (arithmetic mean) score was exactly 80.4. A student who was absent on Monday took the same test on Tuesday and scored 90. The average test was then exactly 81. How many students took the test on Monday?
The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is: (approx.)?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.