A) What is the mean of : 18, 22, 14, 30, 26
x = (18 +22+ 14+ 30+ 26)/5 = 22
(b) What is the sum of the squares of the differences between each data value and the
mean: (data point - x)² or (data point - 22)²
(18-22)² = 16
(22-22)² = 0
(14-22)² = 64
(30-22)² = 64
(26-22)² = 16
Sum = 16+0+64+64+16 = 160
(c) What is the standard deviation
s = √[(∑(x-22)²/(n-1)], where x is the data point, 20 the mean and n =5
√[(∑(x-22)² = 160 and n = 5 (5 data points) then s = 160(5-1) = 160/4 = 40
d) 32, 35, 33, 34, and 36
Rewrite it from smaller to greater:
32, 34, 34, 35 36.
We notice that the range is from 32 to 36 is only 4 (36-32), Where as the range of the
1st pumpkins is 30-14 = 16
Since the spread of the 1st one is by far larger than the 2nd, we can conclude that the
standard deviation of the 1st is greater than the second
Answer: z=-1.00
Step-by-step explanation:
Given : Population mean :
Sample size : n=120 ;
Sample mean: ;
Standard deviation:
Test statistic for population mean:
Hence, the value of the test statistic : z=-1.00
To find out the answer of the two multiplied products with the help of partial products we separate into unit based numbers so as to, for easier calculation and simplification with units of zeroes. So, in this case we are given the product of 4 times of 652.
Here we need to expand this product of higher number to zeroes and take aside the added numbers to come back to the original multiple of a product. That is:
We just separated and expanded the product to be multiplied by removing other units following it. Same goes for other units at Hundredth, tenth and unitary position.
Therefore,
For tenth term.
The terms after splitting and expanding the product before multiplication is:
Multiply the product elements in individual manner and add the elements forged by individual multiplication to get the required solution.
Hope it helps.
Suppose we have the repeat decimal 0.123232323.... or 0.123 with a line over the repeated part (check the diagram)
- The first thing we need to do is identify the part of the decimal that repeats, 23 in our case.
- Second, we are going to assign a variable to our original decimal:
.
- Third, we are going to multiply both sides by a power of ten whose denominator will be the number of repeating digits. We know that we have 2 repeating digits (23), so we are going to multiply both sides by
, and
is just 100; therefore we get:
- fourth, subtract our original equation from the second step from the one from above:
Now we can cancel the repeated decimals to get:
- Last but not least multiply both numerator and denominator by a power of ten equals to the decimal digits in the numerator:
We now know how to convert a repeating decimal to a fraction.