Math  /  Data & Statistics

Question9. Solve the following: b. Find the mean of the first 15 odd natural numbers. 2215=15\rightarrow \frac{22}{15}=15 Ars. c. Compare the mean, median, and mode of the following data: 8,15,15,178,15,15,17, and 20.8+15+15+134020 . \rightarrow 8+15+15+1340
10. The median of observations 4,5,8,11,x+2,x+4,19,26,29,324,5,8,11, x+2, x+4,19,26,29,32 is 13 . Find the value of xx if the values already written in ascending order.
11. The weight (in kg ) of 20 students of a class are as follows: 36,42,45,36,40,45,38,41,36,39,49,43,44,34,50,48,52,41,51,3636,42,45,36,40,45,38,41,36,39,49,43,44,34,50,48,52,41,51,36

Find the mean, median and mode of the given data.
12. A dice was rolled 30 times and the following scores were obtained: 1,6,5,2,6,3,5,1,6,5,3,5,1,3,3,2,6,4,4,4,5,3,4,6,6,2,1,3,5,31,6,5,2,6,3,5,1,6,5,3,5,1,3,3,2,6,4,4,4,5,3,4,6,6,2,1,3,5,3

Find the mode of the given data. 1) Find the mean of the following data: \begin{tabular}{|l|c|c|c|c|c|c|} \hline Agec| & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline No. of students & 23 & 19 & 35 & 18 & 32 & 46 \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The data provided in each problem can be analyzed using standard statistical methods.
2. The mean, median, and mode are well-defined for the given datasets.
3. The values are given in ascending order where specified.

STEP 2

1. Calculate the mean of the first 15 odd natural numbers.
2. Compare the mean, median, and mode of the given dataset.
3. Find the value of x x given the median of the specific dataset.
4. Calculate the mean, median, and mode for the weights of 20 students.
5. Determine the mode of the scores obtained from rolling a dice 30 times.
6. Calculate the mean of the given age data.

STEP 3

Identify the first 15 odd natural numbers and calculate their sum.
The first 15 odd natural numbers are: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
Sum of the first 15 odd natural numbers: 1+3+5+7+9+11+13+15+17+19+21+23+25+27+29 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29

STEP 4

Calculate the mean by dividing the sum by 15.
Mean=1+3+5+7+9+11+13+15+17+19+21+23+25+27+2915 \text{Mean} = \frac{1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29}{15}

STEP 5

Calculate the mean of the dataset 8,15,15,17,208, 15, 15, 17, 20.
Mean=8+15+15+17+205 \text{Mean} = \frac{8 + 15 + 15 + 17 + 20}{5}

STEP 6

Determine the median of the dataset 8,15,15,17,208, 15, 15, 17, 20.
The median is the middle value when the data is ordered: Median=15 \text{Median} = 15

STEP 7

Determine the mode of the dataset 8,15,15,17,208, 15, 15, 17, 20.
The mode is the value that appears most frequently: Mode=15 \text{Mode} = 15

STEP 8

Given the median of the observations 4,5,8,11,x+2,x+4,19,26,29,324, 5, 8, 11, x+2, x+4, 19, 26, 29, 32 is 13, find x x .
Since the median value is the 6th value in the ordered list: x+2=13x=11 x+2 = 13 \Rightarrow x = 11

STEP 9

List the weights of the 20 students: 36,42,45,36,40,45,38,41,36,39,49,43,44,34,50,48,52,41,51,36 36, 42, 45, 36, 40, 45, 38, 41, 36, 39, 49, 43, 44, 34, 50, 48, 52, 41, 51, 36
Calculate the mean weight: Mean=weights20 \text{Mean} = \frac{\sum \text{weights}}{20}

STEP 10

Order the weights to find the median:
34,36,36,36,36,38,39,40,41,41,42,43,44,45,45,48,49,50,51,52 34, 36, 36, 36, 36, 38, 39, 40, 41, 41, 42, 43, 44, 45, 45, 48, 49, 50, 51, 52
The median is the average of the 10th and 11th values: Median=41+422=41.5 \text{Median} = \frac{41 + 42}{2} = 41.5

STEP 11

Identify the mode of the weights, which is the value that appears most frequently:
Mode=36 \text{Mode} = 36

STEP 12

List the scores obtained from rolling a dice 30 times: 1,6,5,2,6,3,5,1,6,5,3,5,1,3,3,2,6,4,4,4,5,3,4,6,6,2,1,3,5,3 1, 6, 5, 2, 6, 3, 5, 1, 6, 5, 3, 5, 1, 3, 3, 2, 6, 4, 4, 4, 5, 3, 4, 6, 6, 2, 1, 3, 5, 3
Determine the mode: Mode=3 and 6 \text{Mode} = 3 \text{ and } 6

STEP 13

Find the mean of the given age data: Age101112131415No. of students231935183246\begin{array}{|l|c|c|c|c|c|c|} \hline \text{Age} & 10 & 11 & 12 & 13 & 14 & 15 \\ \hline \text{No. of students} & 23 & 19 & 35 & 18 & 32 & 46 \\ \hline \end{array}
Calculate the mean: Mean=23×10+19×11+35×12+18×13+32×14+46×1523+19+35+18+32+46 \text{Mean} = \frac{23 \times 10 + 19 \times 11 + 35 \times 12 + 18 \times 13 + 32 \times 14 + 46 \times 15}{23 + 19 + 35 + 18 + 32 + 46}
Solution:
1. Mean of the first 15 odd natural numbers: 15.
2. For 8,15,15,17,208, 15, 15, 17, 20: - Mean: 15 - Median: 15 - Mode: 15
3. Value of x x : 11.
4. For the weights of 20 students: - Mean: 42.45 - Median: 41.5 - Mode: 36
5. Mode of dice rolls: 3 and 6.
6. Mean of age data: 13.17.

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