In today's modern medical arena patients with brain tumor are increasing rapidly with a fast pace and above the par. Detection of brain tumor has become a challenging task to compete with. In this paper an automated method for detecting brain abnormalities and tumor edema has been proposed using sobel edge detection method. Various MRI images have been used as inputs here. Here, first of all the pre-processing of image has been done to cut out any discrepancy in it and then the image has been smoothened using median filter. We have proposed an appropriate method to find threshold value using standard deviation and we get an intensity map. Now we recomputed standard deviation for this intensity map. Using this we will calculate an average intensity of the pixels those are above this standard deviation. Finally, this computed average intensity will be taken as the threshold value to segment the tumor from the original MRI images. The intensity value greater than and equal to the calculated threshold value is set to 255 and less than is set to 0, this segments our abnormal region which is tumor. At last, we use sobel edge detector to identify the border of the tumor region. The outcome of the proposed method improves efficacy and accuracy for detection of brain tumors.