Whats the mean of 464, 194, 414 , 594, 279 , 879, 406, 144 Show All Steps
To find the mean, you need to add up all the numbers in the given set and then divide the sum by the total count of numbers.
So, adding up the numbers:
464 + 194 + 414 + 594 + 279 + 879 + 406 + 144 = 3764
And since there are 8 numbers in the set, the mean is:
3764 / 8 = 470.5
Therefore, the mean of the given set is 470.5.
find the median Show All explanation
To find the median, you need to arrange the numbers in ascending order first.
Arranging the given numbers in ascending order:
144, 194, 279, 406, 414, 464, 594, 879
Now, to find the median, you need to determine the middle value of the set. If the set has an odd number of values, the median is the value in the middle. If the set has an even number of values, the median is the mean of the two middle values.
Since there are 8 numbers in this set, the median will be the mean of the two middle values. These two values are 406 and 414.
To find the median, add these two values and divide by 2:
(406 + 414) / 2 = 820 / 2 = 410
Hence, the median of the given set is 410.
find the mode
To find the mode, you need to determine the number or numbers that appear most frequently in the given set.
The given set of numbers is:
464, 194, 414, 594, 279, 879, 406, 144
In this set, there is only one number that appears more than once, which is 279. Therefore, the mode of the given set is 279.
So, the mode of the given set is 279.
find the range
To find the range, you need to subtract the smallest value from the largest value in the given set.
The given set of numbers is:
464, 194, 414, 594, 279, 879, 406, 144
The smallest value in the set is 144, and the largest value in the set is 879.
To find the range, you subtract the smallest value from the largest value:
879 - 144 = 735
So, the range of the given set is 735.
find the IQR
To find the IQR (Interquartile Range), you need to find the values of the first quartile (Q1) and the third quartile (Q3) of the given set of numbers.
First, we need to arrange the given numbers in ascending order:
144, 194, 279, 406, 414, 464, 594, 879
Next, we determine the median (Q2) of the set. Since there are 8 numbers, the median is the mean of the two middle values, which are 406 and 414.
(Q2) = (406 + 414) / 2 = 820 / 2 = 410
Now, we need to determine the median of the lower half of the set, i.e., the quartile Q1. Q1 is the median of the numbers on the left side of the median (Q2). In this case, the numbers are 144, 194, 279, and 406.
(Q1) = (194 + 279) / 2 = 473 / 2 = 236.5
Lastly, we need to determine the median of the upper half of the set, i.e., the quartile Q3. Q3 is the median of the numbers on the right side of the median (Q2). In this case, the numbers are 414, 464, 594, and 879.
(Q3) = (464 + 594) / 2 = 1058 / 2 = 529
Finally, the IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 529 - 236.5 = 292.5
Therefore, the Interquartile Range (IQR) of the given set is 292.5.