1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sdas [7]
3 years ago
10

Various problems with data collection can cause some observations to be missing. Suppose a data set has 20 cases. Here are the v

alues of the variable x for 10 of these cases: 17, 6, 12, 14, 20, 23, 9, 12, 16, 21 The values for the other ten cases are missing. One way to deal with missing data is called imputation. The basic idea is that missing values are replaced, or imputed, with values that are based on an analysis of the data that are not missing. For a data set with a single variable, the usual choice of a value for imputation is the mean of the values that are not missing. (a) Compute the mean and standard deviation for the 10 cases for which x is not missing. (b) Create a new data set with 20 cases by using imputation where you set the values for the 10 missing cases equal to the mean that you computed in the previous part. Compute the mean and standard deviation for this new data set with 20 cases. (c) Summarize what you have learned about the possible effects of this type of imputation on the mean and the standard deviation.
Mathematics
1 answer:
mr Goodwill [35]3 years ago
4 0

Answer:

a) Mean= 15, standard deviation= 5.1575

b) Mean= 15, standard deviation= 3.6469

c) See below

Step-by-step explanation:

(a) Compute the mean and standard deviation for the 10 cases for which x is not missing.

The mean using the ten known values is

\bar x=\frac{17+6+12+14+20+23+9+12+16+21}{10}=15

The standard deviation is

\small s=\sqrt{\frac{(17-15)^2+(6-15)^2+(12-15)^2+(14-15)^2+(20-15)^2+(23-15)^2+(9-15)^2+(12-15)^2+(16-15)^2+(21-15)^2}{10}}=5.1575

(b) Create a new data set with 20 cases by using imputation where you set the values for the 10 missing cases equal to the mean that you computed in the previous part. Compute the mean and standard deviation for this new data set with 20 cases.

The new data set would be

17, 6, 12, 14, 20, 23, 9, 12, 16, 21, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15

The new mean for this set of values would be then

\bar x=\frac{\displaystyle\sum_{i=1}^{20}x_i}{20}=15

The new standard deviation is now

s=\sqrt{\frac{\displaystyle\sum_{i=1}^{20}(x_i-\bar x)^2}{20}}=3.6469

(c) Summarize what you have learned about the possible effects of this type of imputation on the mean and the standard deviation.

Obviously, this way of imputation is somewhat arbitrary and will produce a set of data undoubtedly skewed.  

It could possibly be a sensible way of imputing data if the amount of missing data is very little compared to the whole set, for example one or two data in a set of 100, but in this case we have 50% of missing data and it makes no sense this procedure.

You might be interested in
A table is 4 ft high. A model of the table is 6 in. high. What is the ratio of the height of the actual table to the height of t
Sliva [168]

Answer:

8:1

Step-by-step explanation:

the actual table's height in inches is 4*12 = 48 inches.

48/6 = 8

so the ratio is 8:1.

5 0
3 years ago
Read 2 more answers
Fill in the blank. The centroid is (blank) of the distance from each vertex to the midpoint of the opposite side.
Andre45 [30]

Step-by-step explanation:

.

The centroid is 2/3 of the opposite side. of the distance from each vertex to the midpoint. 8. To inscribe a circle about a triangle, you use the.

5 pages·2 MB

7 0
3 years ago
Will positive numbers always have a higher absolute value than negative numbers?
Reika [66]
-I5I=-5 vs. I-5I= 5

The absolute value will stay the same for both negative and positive. The result will change depending on where you put your absolute value signs.
6 0
3 years ago
Find the values of the variables for which ABCD must be a parallelogram
sleet_krkn [62]

Answer:

y=5 and x=4

Step-by-step explanation:

So,the diagonals of a parallelogram bisect each other..

therefore,we have our two eqn

4x-2=3y-1------------(i)

3y-3=3x

or,y-1=x----------(ii)

Now,simply substitute value of x in eqn (i)

4(y-1)-2=3y-1

or,4y-4-2=3y-1

or,y=5

Again,substitute y=5 in eqn (ii)

5-1=x

therefore,

x=5

Hope it helps you!!!

4 0
3 years ago
How many terms are in the following expression?<br> -4a +8C -4b +3
mart [117]

Answer: 4 terms

Step-by-step explanation:

-4a , 8c, -4b, and 3

8 0
3 years ago
Other questions:
  • Katie’s water bottle contains 1 7/8 liters. She uses her bottle to fill sue’s. When she is done, her bottle contains 1/4 liter.
    12·1 answer
  • Polygons QRST and Q’R’S’T’ are shown on the coordinate grid: A coordinate plane with two polygons is shown. Polygon QRST has ver
    10·1 answer
  • Need help with this question please!
    14·1 answer
  • Math help please urgent
    12·2 answers
  • Kathy distributes jelly beans among her friends. Alia gets 42 fewer jelly beans than Kelly, who gets 33 jelly beans. How many je
    7·2 answers
  • Mrs. Trotta drives a total of 378 miles over 6 days. She drives the same amount of miles each day. How many miles does Mrs. Trot
    12·1 answer
  • What is x y and z value
    7·2 answers
  • 4.
    14·1 answer
  • Latasia ran the 2 mile run at a track meet. How many feet is that?
    6·2 answers
  • Pls help math!! :(!!!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!