RS Aggarwal Test: Statistics - Class 10 MCQ

In statistics, a central tendency is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages. So we have 3 measures of central tendencies namely, mean , median and mode. So mean is the answer as the other three options are the components of the given distribution.

Class mark is the mean of the upper limit and lower limit of the class. The class mark is a specific point in the center of the interval in a frequency distribution table. It is defined as the average of the upper and lower class limits. So formula is Class mark =

We have Mean = 

mean = ∑fixi
              ∑fi
mean = 10x2+12x3+15x7+25x8
                      2+3+7+8
mean = 20+36+105+200
                       20
mean = 361/20 =18.05

Mode is the value with the maximum frequency. Thus, it can be determined from the graph.
Median is the middle value of the data. Thus, it can be determined from the graph.
Mean is the ratio of sum of all data values and the total number of values. Thus, it cannot be determined graphically.
The bell curve or standard deviation graph is used to visualise the spread of data. The standard deviation tells how much the data is clustered around the mean of the data. Lower standard deviation tells that the data is less spread and higher standard deviation tells that data is more spread.

Given that the median of the data is 40, we can determine the value of p as follows:

Step 1: Identify the Cumulative Frequency

Step 2: Determine the Median Class

The median is given as 40, which lies in the class interval 30-60. Thus, the median class is 30-60.

Step 3: Apply the Median Formula

The formula for the median of grouped data is:

Median = L + ( (N/2 - F) / f ) * h

• L = Lower limit of the median class = 30
• N = Total frequency = 5 + 15 + 30 + p + 2 = 52 + p
• F = Cumulative frequency of the class before the median class = 20
• f = Frequency of the median class = 30
• h = Class width = 30 (for class 30-60)

Step 4: Substitute Values into the Formula

Given that the median is 40:

40 = 30 + ( (52 + p) / 2 - 20) / 30 ) * 30

Step 5: Simplify the Equation

1. Calculate (52 + p) / 2:

   (52 + p) / 2 = 26 + p / 2

2. Substitute into the equation:

   40 = 30 + ( (26 + p / 2 - 20) / 30 ) * 30

3. Simplify inside the parentheses:

   40 = 30 + (6 + p / 2)

4. Subtract 30 from both sides:

   10 = 6 + p / 2

5. Subtract 6 from both sides:

   4 = p / 2

6. Multiply both sides by 2:

   p = 8

Conclusion

The value of p is: 8

Mean = Mode + 3/2 [Median – Mode]
Mean= Mode+3/2 Median-3/2Mode
2 Mean=2 Mode+3 Median-3 Mode
3 Median=2 Mean + Mode
So C is the correct answer.

f₁ is the frequency of the modal class.So , f₀ is the frequency of the class preceding the modal class. So C option is correct.

The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Mean = Sum of Observations/Total No of Observations

Mean = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 ÷ 10

Mean = 55/10

Mean = 5.5

Step-by-step explanation:mean=2+3+5+7+11+13+17+19+23+29/10

Mean=129/10

Mean=12.9

The mean is the average of the numbers.
So, Mean = 
Mean= =342/9=38

Natural numbers start from 1
First ten natural odd numbers=1,3,5,7,9,11,13,15,17,19
Mean = 
So mean is 10.

We have first ten multiples of 6 as follows:
6,12,18,24,30,36,42,48,54,60

To find the mean of all the factors of 24:

- List the factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
- Sum the factors: (1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 = 60).
- Count the factors: There are 8 factors.
- Calculate the mean: Sum of the factors/ number of the factors = 60/8 = 7.5
Thus, the mean of all the factors is 7.5. The correct answer is A: 7.5.

The mean is the average of the numbers.
So, Mean = 
Mean= 351/9=39

We have mean = 
Mean = 
Now each value is increased by 5
Mean = 
+5=65+5=70
Hence the mean is 70