please help me to solved these questions calculate the median for the following group data class interval 1-10 , 11-20,21-30, 31-40,41-50 frequency 3 ,12,16,14,5 please give me the answers of these questions i have tried but my answer is 26.625 are came but the actual answer is 26.75 step by step explanations
Answers
Answer:
Question 1:
The marks scored by 40 candidates in an examination (out of 100) is given below:
75, 65, 57, 50, 32, 54, 75, 67, 75, 88, 80, 42, 40, 41, 34, 78, 43, 61,
42, 46, 68, 52, 43, 49, 59, 49, 67, 34, 33, 87, 97, 47, 46, 54, 48, 45,
51, 47, 41, 43.
Prepare a frequency distribution table with the class size 10. Take the class intervals as (30 - 39), (40 - 49), … and answer the following question:
(a) Which class intervals have highest and lowest frequency?
(b) Write the upper and lower limits of the class interval 30-39.
(c) What is the range of he given distribution?
ANSWER:
The frequency distribution table for the given marks can be drawn as:
(i) The class interval (40−49) has the highest frequency and the class interval (90−99) has the lowest frequency.
(ii) In the class interval (30−39), the lower limit is 30 − 0.5 = 29.5 and the upper limit is
39 + 0.5 = 39.5.
(iii) The range of the given distribution is 97− 32 = 65.Question 2:
Prepare the frequency distribution table for the given set of scores:
39, 16, 30, 37, 53, 15, 16, 60, 58, 26, 28, 19, 20, 12, 14, 24, 59,
21, 57, 38, 25, 36, 34, 15, 25, 41, 52, 45, 60, 63, 18, 26, 43, 36, 18,
27, 59, 63, 46, 48, 25, 33, 46, 27, 46, 42, 48, 35, 64, 24.
Take class intervals as (10 -20), (20 − 30), … and answer the following:
(i) What does the frequency corresponding to the third class interval mean?
(ii) What is the size of each class interval? Find the midpoint of the class interval 30- 40.
(iii) What is the range of the given set of scores?
ANSWER:
The frequency distribution table for the given scores can be drawn as:
(i) The frequency corresponding to the third class interval (30−40) is 9.
(ii) The size of each class interval is 10 and the midpoint of the class interval (30−40) is
(iii) The range of the given scores is 64 − 12 = 52Question 1:
Draw a histogram to represent the following frequency distribution.
Class – Interval
Frequency
20 – 25
5
25 – 30
10
30 – 35
18
35 – 40
14
40 – 45
12
ANSWER:
The given frequency distribution is:
To draw a histogram for this frequency distribution, we follow the steps below.
Step 1: We draw the x and y-axes.
Step 2: We choose a proper scale for the axes. Let 1 cm = 5 on the x-axis and 1 cm = 5 on the y-axis.
Step 3: We mark the class intervals on the x-axis as (20−25), (25−30), (30−35), etc.
Step 4: We draw a rectangle of height 5 cm on the first class interval (20−25).
Step 5: We draw a second rectangle of height 10 cm on the second class interval (25−30). We follow the same procedure for the remaining class intervals and the corresponding frequencies. Thus, we get the required histogram for the given frequency distribution as shown below.